AP Calculus AB Flashcards: Rates Of Change In Applied Concepts

Study Rates Of Change In Applied Concepts in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Calculus AB

Rates Of Change In Applied Concepts

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QUESTION

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Identify the derivative of $y = 3x^3 + 5x^2 - x$ .

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ANSWER

$9x^2 + 10x - 1$ . Power rule: $9x^2$ from $3x^3$ , $10x$ from $5x^2$ , $-1$ from $-x$ .

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What this deck covers

This deck focuses on Rates Of Change In Applied Concepts, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Identify the derivative of $y = 3x^3 + 5x^2 - x$ .

Answer: $9x^2 + 10x - 1$ . Power rule: $9x^2$ from $3x^3$ , $10x$ from $5x^2$ , $-1$ from $-x$ .

Flashcard 2: What is the derivative of the function $f(x) = x^5 - 4x^3 + 2$ ?

Answer: $5x^4 - 12x^2$ . Power rule: $5x^4$ from $x^5$ and $-12x^2$ from $-4x^3$ .

Flashcard 3: Determine the derivative of the function $y = \frac{2}{x^2}$ .

Answer: $-\frac{4}{x^3}$ . Power rule: $2x^{-2}$ becomes $-4x^{-3}$ .

Flashcard 4: What is the derivative of $h(x) = \frac{1}{x^2}$ ?

Answer: $-\frac{2}{x^3}$ . Power rule: $x^{-2}$ becomes $-2x^{-3}$ .

Flashcard 5: Determine the derivative of $f(x) = \frac{3}{x}$ .

Answer: $-\frac{3}{x^2}$ . Constant multiple rule: $3 \cdot (-x^{-2}) = -3x^{-2}$ .

Flashcard 6: What is the derivative of $f(x) = x^4 + 2x^2 + 1$ ?

Answer: $4x^3 + 4x$ . Power rule: $4x^3$ from $x^4$ and $4x$ from $2x^2$ .

Flashcard 7: Find the derivative of $y = 2x^3 + 3x^2 - 5x + 1$ .

Answer: $6x^2 + 6x - 5$ . Power rule applied: $6x^2$ , $6x$ , and $-5$ from each term.

Flashcard 8: Identify the rate of change of the volume of a rectangular prism with respect to its height.

Answer: Area of base. Volume formula is base area times height.

Flashcard 9: Find the derivative of $h(x) = 7x^5 - 3x^2 + 1$ .

Answer: $35x^4 - 6x$ . Power rule: $35x^4$ from $7x^5$ and $-6x$ from $-3x^2$ .

Flashcard 10: What is the derivative of $h(x) = \frac{1}{x^5}$ ?

Answer: $-\frac{5}{x^6}$ . Power rule: $x^{-5}$ becomes $-5x^{-6}$ .

Flashcard 11: What is the derivative of the function $f(x) = \frac{2}{x^3}$ ?

Answer: $-\frac{6}{x^4}$ . Power rule: $2x^{-3}$ becomes $-6x^{-4}$ .

Flashcard 12: What is the rate of change of the surface area of a sphere with respect to its radius?

Answer: $8\pi r$ . Derivative of sphere surface area $4\pi r^2$ .

Flashcard 13: Identify the rate of change of the area of a rectangle with respect to its width.

Answer: Length. For rectangle area $lw$ , derivative with respect to width is length.

Flashcard 14: Determine the derivative of $f(x) = 4x^2 - 3x + 7$ .

Answer: $8x - 3$ . Power rule: $8x$ from $4x^2$ and $-3$ from $-3x$ .

Flashcard 15: What is the derivative of $f(x) = 2x^3 - x^2 + 3$ ?

Answer: $6x^2 - 2x$ . Power rule: $6x^2$ from $2x^3$ and $-2x$ from $-x^2$ .

Flashcard 16: Identify the derivative of $y = \frac{1}{x} + x^2$ .

Answer: $-\frac{1}{x^2} + 2x$ . Combine derivatives: $-x^{-2}$ and $2x$ terms.

Flashcard 17: What is the rate of change of the area of a rectangle with respect to its length?

Answer: Width. For rectangle area $lw$ , derivative with respect to length is width.

Flashcard 18: What is the derivative of the area of a circle with respect to its radius?

Answer: $2\pi r$ . Derivative of area $\pi r^2$ gives the circumference formula.

Flashcard 19: Identify the derivative of $y = 6x^2 + 4x - 5$ .

Answer: $12x + 4$ . Power rule: $12x$ from $6x^2$ and $4$ from $4x$ .

Flashcard 20: What is the derivative of the function $h(x) = \frac{2}{x^3}$ ?

Answer: $-\frac{6}{x^4}$ . Power rule: $2x^{-3}$ becomes $-6x^{-4}$ .

Flashcard 21: What is the derivative of $y = x^3 + x^2$ with respect to $x$ ?

Answer: $3x^2 + 2x$ . Apply power rule: $3x^2$ from $x^3$ and $2x$ from $x^2$ .

Flashcard 22: Find the rate of change of the circumference of a circle with respect to its radius.

Answer: $2\pi$ . Derivative of circumference $2\pi r$ is constant $2\pi$ .

Flashcard 23: What is the rate of change of the perimeter of a square with respect to its side length?

Answer:

Each side contributes 1 to perimeter, so total rate is 4.

Flashcard 24: What is the rate of change of the surface area of a sphere with respect to its radius?

Answer: $8\pi r$ . Derivative of sphere surface area $4\pi r^2$ .

Flashcard 25: Find the derivative of $y = 4x^4 - 3x^3 + x - 7$ .

Answer: $16x^3 - 9x^2 + 1$ . Power rule applied to each term: $16x^3$ , $-9x^2$ , $1$ .

Flashcard 26: Find the rate of change of the volume of a cylinder with respect to its height.

Answer: $\pi r^2$ . For cylinder volume $\pi r^2 h$ , derivative with respect to height.

Flashcard 27: What is the derivative of the function $f(x) = \frac{2}{x^3}$ ?

Answer: $-\frac{6}{x^4}$ . Power rule: $2x^{-3}$ becomes $-6x^{-4}$ .

Flashcard 28: Find the rate of change of the circumference of a circle with respect to its radius.

Answer: $2\pi$ . Derivative of circumference $2\pi r$ is constant $2\pi$ .

Flashcard 29: What is the derivative of the function $g(x) = \frac{1}{x^4}$ ?

Answer: $-\frac{4}{x^5}$ . Power rule: $x^{-4}$ becomes $-4x^{-5}$ .

Flashcard 30: Find the derivative of $h(x) = 7x^5 - 3x^2 + 1$ .

Answer: $35x^4 - 6x$ . Power rule: $35x^4$ from $7x^5$ and $-6x$ from $-3x^2$ .

Flashcard 31: Identify the derivative of the function $g(x) = \frac{1}{x}$ .

Answer: $-\frac{1}{x^2}$ . Power rule: $x^{-1}$ becomes $-x^{-2}$ .

Flashcard 32: Find the rate of change of the area of a square with side length $s$ .

Answer: $2s$ . Derivative of area $s^2$ gives rate of change.

Flashcard 33: What is the derivative of $y = x^3 + x^2$ with respect to $x$ ?

Answer: $3x^2 + 2x$ . Apply power rule: $3x^2$ from $x^3$ and $2x$ from $x^2$ .

Flashcard 34: What is the derivative of $f(x) = x^3 - 2x + 4$ with respect to $x$ ?

Answer: $3x^2 - 2$ . Power rule: $3x^2$ from $x^3$ and $-2$ from $-2x$ .

Flashcard 35: Determine the derivative of $f(x) = 4x^2 - 3x + 7$ .

Answer: $8x - 3$ . Power rule: $8x$ from $4x^2$ and $-3$ from $-3x$ .

Flashcard 36: What is the formula for the derivative of $y = \frac{1}{x^3}$ ?

Answer: $-\frac{3}{x^4}$ . Power rule: $x^{-3}$ becomes $-3x^{-4}$ .

Flashcard 37: What is the rate of change of the area of a rectangle with respect to its length?

Answer: Width. For rectangle area $lw$ , derivative with respect to length is width.

Flashcard 38: What is the derivative of the area of a circle with respect to its radius?

Answer: $2\pi r$ . Derivative of area $\pi r^2$ gives the circumference formula.

Flashcard 39: Determine the derivative of the function $y = \frac{2}{x^2}$ .

Answer: $-\frac{4}{x^3}$ . Power rule: $2x^{-2}$ becomes $-4x^{-3}$ .

Flashcard 40: Identify the rate of change of the volume of a rectangular prism with respect to its height.

Answer: Area of base. Volume formula is base area times height.

Flashcard 41: What is the derivative of $h(x) = 5x^3 - 4x + 8$ ?

Answer: $15x^2 - 4$ . Power rule: $15x^2$ from $5x^3$ and $-4$ from $-4x$ .

Flashcard 42: What is the derivative of the function $g(x) = \frac{1}{x^4}$ ?

Answer: $-\frac{4}{x^5}$ . Power rule: $x^{-4}$ becomes $-4x^{-5}$ .

Flashcard 43: What is the derivative of $f(x) = 2x^3 - x^2 + 3$ ?

Answer: $6x^2 - 2x$ . Power rule: $6x^2$ from $2x^3$ and $-2x$ from $-x^2$ .

Flashcard 44: Find the derivative of $y = 2x^3 + 3x^2 - 5x + 1$ .

Answer: $6x^2 + 6x - 5$ . Power rule applied: $6x^2$ , $6x$ , and $-5$ from each term.

Flashcard 45: Determine the derivative of $g(x) = x^2 - \frac{1}{x}$ .

Answer: $2x + \frac{1}{x^2}$ . Sum rule: $2x$ from $x^2$ plus $x^{-2}$ from $-x^{-1}$ .

Flashcard 46: What is the derivative of $h(x) = 5x^3 - 4x + 8$ ?

Answer: $15x^2 - 4$ . Power rule: $15x^2$ from $5x^3$ and $-4$ from $-4x$ .

Flashcard 47: Identify the derivative of $y = 3x^3 + 5x^2 - x$ .

Answer: $9x^2 + 10x - 1$ . Power rule: $9x^2$ from $3x^3$ , $10x$ from $5x^2$ , $-1$ from $-x$ .

Flashcard 48: What is the rate of change of the surface area of a cube with respect to its side length?

Answer: $12s$ . Derivative of surface area $6s^2$ with respect to side.

Flashcard 49: What is the derivative of $h(x) = \frac{1}{x^5}$ ?

Answer: $-\frac{5}{x^6}$ . Power rule: $x^{-5}$ becomes $-5x^{-6}$ .

Flashcard 50: What is the derivative of the function $g(x) = x^4 - \frac{1}{x^2}$ ?

Answer: $4x^3 + \frac{2}{x^3}$ . Power rule: $4x^3$ from $x^4$ and $2x^{-3}$ from $-x^{-2}$ .

Flashcard 51: What is the derivative of the function $g(x) = x^4 - \frac{1}{x^2}$ ?

Answer: $4x^3 + \frac{2}{x^3}$ . Power rule: $4x^3$ from $x^4$ and $2x^{-3}$ from $-x^{-2}$ .

Flashcard 52: Identify the rate of change of the volume of a cube with respect to its side length.

Answer: $3s^2$ . Derivative of volume $s^3$ with respect to side length.

Flashcard 53: Find the rate of change of the area of a square with side length $s$ .

Answer: $2s$ . Derivative of area $s^2$ gives rate of change.

Flashcard 54: Identify the rate of change of the area of a rectangle with respect to its width.

Answer: Length. For rectangle area $lw$ , derivative with respect to width is length.

Flashcard 55: What is the formula for the rate of change of the volume of a sphere with respect to its radius?

Answer: $4\pi r^2$ . Derivative of sphere volume $\frac{4}{3}\pi r^3$ .

Flashcard 56: What is the formula for the derivative of $y = \frac{1}{x^3}$ ?

Answer: $-\frac{3}{x^4}$ . Power rule: $x^{-3}$ becomes $-3x^{-4}$

Flashcard 57: What is the derivative of $g(x) = x^3 + \frac{1}{x}$ ?

Answer: $3x^2 - \frac{1}{x^2}$ . Power rule: $3x^2$ from $x^3$ and $-x^{-2}$ from $x^{-1}$ .

Flashcard 58: Determine the derivative of $f(x) = \frac{3}{x}$ .

Answer: $-\frac{3}{x^2}$ . Constant multiple rule: $3 \cdot (-x^{-2}) = -3x^{-2}$ .

Flashcard 59: What is the derivative of the function $h(x) = \frac{2}{x^3}$ ?

Answer: $-\frac{6}{x^4}$ . Power rule: $2x^{-3}$ becomes $-6x^{-4}$ .

Flashcard 60: Identify the derivative of $y = \frac{1}{x} + x^2$ .

Answer: $-\frac{1}{x^2} + 2x$ . Combine derivatives: $-x^{-2}$ and $2x$ terms.

Flashcard 61: What is the derivative of $h(x) = \frac{1}{x^2}$ ?

Answer: $-\frac{2}{x^3}$ . Power rule: $x^{-2}$ becomes $-2x^{-3}$ .

Flashcard 62: Determine the derivative of $g(x) = x^2 - \frac{1}{x}$ .

Answer: $2x + \frac{1}{x^2}$ . Sum rule: $2x$ from $x^2$ plus $x^{-2}$ from $-x^{-1}$ .

Flashcard 63: Identify the rate of change of the volume of a cube with respect to its side length.

Answer: $3s^2$ . Derivative of volume $s^3$ with respect to side length.

Flashcard 64: Identify the derivative of the function $g(x) = \frac{1}{x}$ .

Answer: $-\frac{1}{x^2}$ . Power rule: $x^{-1}$ becomes $-x^{-2}$ .

Flashcard 65: What is the derivative of $f(x) = x^3 - 2x + 4$ with respect to $x$ ?

Answer: $3x^2 - 2$ . Power rule: $3x^2$ from $x^3$ and $-2$ from $-2x$ .

Flashcard 66: What is the derivative of the function $f(x) = x^5 - 4x^3 + 2$ ?

Answer: $5x^4 - 12x^2$ . Power rule: $5x^4$ from $x^5$ and $-12x^2$ from $-4x^3$ .

Flashcard 67: What is the formula for the rate of change of the volume of a sphere with respect to its radius?

Answer: $4\pi r^2$ . Derivative of sphere volume $\frac{4}{3}\pi r^3$ .

Flashcard 68: Identify the derivative of $y = 6x^2 + 4x - 5$ .

Answer: $12x + 4$ . Power rule: $12x$ from $6x^2$ and $4$ from $4x$ .

Flashcard 69: What is the rate of change of the surface area of a cube with respect to its side length?

Answer: $12s$ . Derivative of surface area $6s^2$ with respect to side.

Flashcard 70: Determine the derivative of the function $f(x) = 5x^4 - 3x^2 + 7$ .

Answer: $20x^3 - 6x$ . Power rule applied: $20x^3$ from $5x^4$ and $-6x$ from $-3x^2$ .

Flashcard 71: Find the rate of change of the volume of a cylinder with respect to its height.

Answer: $\pi r^2$ . For cylinder volume $\pi r^2 h$ , derivative with respect to height.

Flashcard 72: What is the derivative of $f(x) = x^4 + 2x^2 + 1$ ?

Answer: $4x^3 + 4x$ . Power rule: $4x^3$ from $x^4$ and $4x$ from $2x^2$ .

Flashcard 73: Find the derivative of $y = 4x^4 - 3x^3 + x - 7$ .

Answer: $16x^3 - 9x^2 + 1$ . Power rule applied to each term: $16x^3$ , $-9x^2$ , $1$ .

Flashcard 74: What is the derivative of $g(x) = x^3 + \frac{1}{x}$ ?

Answer: $3x^2 - \frac{1}{x^2}$ . Power rule: $3x^2$ from $x^3$ and $-x^{-2}$ from $x^{-1}$ .

Flashcard 75: Determine the derivative of the function $f(x) = 5x^4 - 3x^2 + 7$ .

Answer: $20x^3 - 6x$ . Power rule applied: $20x^3$ from $5x^4$ and $-6x$ from $-3x^2$ .

Flashcard 76: What is the rate of change of the perimeter of a square with respect to its side length?

Answer:

Each side contributes 1 to perimeter, so total rate is 4.

AP Calculus AB Flashcards: Rates Of Change In Applied Concepts

Rates Of Change In Applied Concepts

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Identify the derivative of y=3x3+5x2−xy = 3x^3 + 5x^2 - xy=3x3+5x2−x.

Flashcard 2: What is the derivative of the function f(x)=x5−4x3+2f(x) = x^5 - 4x^3 + 2f(x)=x5−4x3+2?

Flashcard 3: Determine the derivative of the function y=2x2y = \frac{2}{x^2}y=x22​.

Flashcard 4: What is the derivative of h(x)=1x2h(x) = \frac{1}{x^2}h(x)=x21​?

Flashcard 5: Determine the derivative of f(x)=3xf(x) = \frac{3}{x}f(x)=x3​.

Flashcard 6: What is the derivative of f(x)=x4+2x2+1f(x) = x^4 + 2x^2 + 1f(x)=x4+2x2+1?

Flashcard 7: Find the derivative of y=2x3+3x2−5x+1y = 2x^3 + 3x^2 - 5x + 1y=2x3+3x2−5x+1.

Flashcard 8: Identify the rate of change of the volume of a rectangular prism with respect to its height.

Flashcard 9: Find the derivative of h(x)=7x5−3x2+1h(x) = 7x^5 - 3x^2 + 1h(x)=7x5−3x2+1.

Flashcard 10: What is the derivative of h(x)=1x5h(x) = \frac{1}{x^5}h(x)=x51​?

Flashcard 11: What is the derivative of the function f(x)=2x3f(x) = \frac{2}{x^3}f(x)=x32​?

Flashcard 12: What is the rate of change of the surface area of a sphere with respect to its radius?

Flashcard 13: Identify the rate of change of the area of a rectangle with respect to its width.

Flashcard 14: Determine the derivative of f(x)=4x2−3x+7f(x) = 4x^2 - 3x + 7f(x)=4x2−3x+7.

Flashcard 15: What is the derivative of f(x)=2x3−x2+3f(x) = 2x^3 - x^2 + 3f(x)=2x3−x2+3?

Flashcard 16: Identify the derivative of y=1x+x2y = \frac{1}{x} + x^2y=x1​+x2.

Flashcard 17: What is the rate of change of the area of a rectangle with respect to its length?

Flashcard 18: What is the derivative of the area of a circle with respect to its radius?

Flashcard 19: Identify the derivative of y=6x2+4x−5y = 6x^2 + 4x - 5y=6x2+4x−5.

Flashcard 20: What is the derivative of the function h(x)=2x3h(x) = \frac{2}{x^3}h(x)=x32​?

Flashcard 21: What is the derivative of y=x3+x2y = x^3 + x^2y=x3+x2 with respect to xxx?

Flashcard 22: Find the rate of change of the circumference of a circle with respect to its radius.

Flashcard 23: What is the rate of change of the perimeter of a square with respect to its side length?

Flashcard 24: What is the rate of change of the surface area of a sphere with respect to its radius?

Flashcard 25: Find the derivative of y=4x4−3x3+x−7y = 4x^4 - 3x^3 + x - 7y=4x4−3x3+x−7.

Flashcard 26: Find the rate of change of the volume of a cylinder with respect to its height.

Flashcard 27: What is the derivative of the function f(x)=2x3f(x) = \frac{2}{x^3}f(x)=x32​?

Flashcard 28: Find the rate of change of the circumference of a circle with respect to its radius.

Flashcard 29: What is the derivative of the function g(x)=1x4g(x) = \frac{1}{x^4}g(x)=x41​?

Flashcard 30: Find the derivative of h(x)=7x5−3x2+1h(x) = 7x^5 - 3x^2 + 1h(x)=7x5−3x2+1.

Flashcard 31: Identify the derivative of the function g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 32: Find the rate of change of the area of a square with side length sss.

Flashcard 33: What is the derivative of y=x3+x2y = x^3 + x^2y=x3+x2 with respect to xxx?

Flashcard 34: What is the derivative of f(x)=x3−2x+4f(x) = x^3 - 2x + 4f(x)=x3−2x+4 with respect to xxx?

Flashcard 35: Determine the derivative of f(x)=4x2−3x+7f(x) = 4x^2 - 3x + 7f(x)=4x2−3x+7.

Flashcard 36: What is the formula for the derivative of y=1x3y = \frac{1}{x^3}y=x31​?

Flashcard 37: What is the rate of change of the area of a rectangle with respect to its length?

Flashcard 38: What is the derivative of the area of a circle with respect to its radius?

Flashcard 39: Determine the derivative of the function y=2x2y = \frac{2}{x^2}y=x22​.

Flashcard 40: Identify the rate of change of the volume of a rectangular prism with respect to its height.

Flashcard 41: What is the derivative of h(x)=5x3−4x+8h(x) = 5x^3 - 4x + 8h(x)=5x3−4x+8?

Flashcard 42: What is the derivative of the function g(x)=1x4g(x) = \frac{1}{x^4}g(x)=x41​?

Flashcard 43: What is the derivative of f(x)=2x3−x2+3f(x) = 2x^3 - x^2 + 3f(x)=2x3−x2+3?

Flashcard 44: Find the derivative of y=2x3+3x2−5x+1y = 2x^3 + 3x^2 - 5x + 1y=2x3+3x2−5x+1.

Flashcard 45: Determine the derivative of g(x)=x2−1xg(x) = x^2 - \frac{1}{x}g(x)=x2−x1​.

Flashcard 46: What is the derivative of h(x)=5x3−4x+8h(x) = 5x^3 - 4x + 8h(x)=5x3−4x+8?

Flashcard 47: Identify the derivative of y=3x3+5x2−xy = 3x^3 + 5x^2 - xy=3x3+5x2−x.

Flashcard 48: What is the rate of change of the surface area of a cube with respect to its side length?

Flashcard 49: What is the derivative of h(x)=1x5h(x) = \frac{1}{x^5}h(x)=x51​?

Flashcard 50: What is the derivative of the function g(x)=x4−1x2g(x) = x^4 - \frac{1}{x^2}g(x)=x4−x21​?

Flashcard 51: What is the derivative of the function g(x)=x4−1x2g(x) = x^4 - \frac{1}{x^2}g(x)=x4−x21​?

Flashcard 52: Identify the rate of change of the volume of a cube with respect to its side length.

Flashcard 53: Find the rate of change of the area of a square with side length sss.

Flashcard 54: Identify the rate of change of the area of a rectangle with respect to its width.

Flashcard 55: What is the formula for the rate of change of the volume of a sphere with respect to its radius?

Flashcard 56: What is the formula for the derivative of y=1x3y = \frac{1}{x^3}y=x31​?

Flashcard 57: What is the derivative of g(x)=x3+1xg(x) = x^3 + \frac{1}{x}g(x)=x3+x1​?

Flashcard 58: Determine the derivative of f(x)=3xf(x) = \frac{3}{x}f(x)=x3​.

Flashcard 59: What is the derivative of the function h(x)=2x3h(x) = \frac{2}{x^3}h(x)=x32​?

Flashcard 60: Identify the derivative of y=1x+x2y = \frac{1}{x} + x^2y=x1​+x2.

Flashcard 61: What is the derivative of h(x)=1x2h(x) = \frac{1}{x^2}h(x)=x21​?

Flashcard 62: Determine the derivative of g(x)=x2−1xg(x) = x^2 - \frac{1}{x}g(x)=x2−x1​.

Flashcard 63: Identify the rate of change of the volume of a cube with respect to its side length.

Flashcard 64: Identify the derivative of the function g(x)=1xg(x) = \frac{1}{x}g(x)=x1​.

Flashcard 65: What is the derivative of f(x)=x3−2x+4f(x) = x^3 - 2x + 4f(x)=x3−2x+4 with respect to xxx?

Flashcard 66: What is the derivative of the function f(x)=x5−4x3+2f(x) = x^5 - 4x^3 + 2f(x)=x5−4x3+2?

Flashcard 67: What is the formula for the rate of change of the volume of a sphere with respect to its radius?

Flashcard 68: Identify the derivative of y=6x2+4x−5y = 6x^2 + 4x - 5y=6x2+4x−5.

Flashcard 69: What is the rate of change of the surface area of a cube with respect to its side length?

Flashcard 70: Determine the derivative of the function f(x)=5x4−3x2+7f(x) = 5x^4 - 3x^2 + 7f(x)=5x4−3x2+7.

Flashcard 71: Find the rate of change of the volume of a cylinder with respect to its height.

Flashcard 72: What is the derivative of f(x)=x4+2x2+1f(x) = x^4 + 2x^2 + 1f(x)=x4+2x2+1?

Flashcard 73: Find the derivative of y=4x4−3x3+x−7y = 4x^4 - 3x^3 + x - 7y=4x4−3x3+x−7.

Flashcard 74: What is the derivative of g(x)=x3+1xg(x) = x^3 + \frac{1}{x}g(x)=x3+x1​?

Flashcard 75: Determine the derivative of the function f(x)=5x4−3x2+7f(x) = 5x^4 - 3x^2 + 7f(x)=5x4−3x2+7.

Flashcard 1: Identify the derivative of $y = 3x^3 + 5x^2 - x$ .

Flashcard 2: What is the derivative of the function $f(x) = x^5 - 4x^3 + 2$ ?

Flashcard 3: Determine the derivative of the function $y = \frac{2}{x^2}$ .

Flashcard 4: What is the derivative of $h(x) = \frac{1}{x^2}$ ?

Flashcard 5: Determine the derivative of $f(x) = \frac{3}{x}$ .

Flashcard 6: What is the derivative of $f(x) = x^4 + 2x^2 + 1$ ?

Flashcard 7: Find the derivative of $y = 2x^3 + 3x^2 - 5x + 1$ .

Flashcard 9: Find the derivative of $h(x) = 7x^5 - 3x^2 + 1$ .

Flashcard 10: What is the derivative of $h(x) = \frac{1}{x^5}$ ?

Flashcard 11: What is the derivative of the function $f(x) = \frac{2}{x^3}$ ?

Flashcard 14: Determine the derivative of $f(x) = 4x^2 - 3x + 7$ .

Flashcard 15: What is the derivative of $f(x) = 2x^3 - x^2 + 3$ ?

Flashcard 16: Identify the derivative of $y = \frac{1}{x} + x^2$ .

Flashcard 19: Identify the derivative of $y = 6x^2 + 4x - 5$ .

Flashcard 20: What is the derivative of the function $h(x) = \frac{2}{x^3}$ ?

Flashcard 21: What is the derivative of $y = x^3 + x^2$ with respect to $x$ ?

Flashcard 25: Find the derivative of $y = 4x^4 - 3x^3 + x - 7$ .

Flashcard 27: What is the derivative of the function $f(x) = \frac{2}{x^3}$ ?

Flashcard 29: What is the derivative of the function $g(x) = \frac{1}{x^4}$ ?

Flashcard 30: Find the derivative of $h(x) = 7x^5 - 3x^2 + 1$ .

Flashcard 31: Identify the derivative of the function $g(x) = \frac{1}{x}$ .

Flashcard 32: Find the rate of change of the area of a square with side length $s$ .

Flashcard 33: What is the derivative of $y = x^3 + x^2$ with respect to $x$ ?

Flashcard 34: What is the derivative of $f(x) = x^3 - 2x + 4$ with respect to $x$ ?

Flashcard 35: Determine the derivative of $f(x) = 4x^2 - 3x + 7$ .

Flashcard 36: What is the formula for the derivative of $y = \frac{1}{x^3}$ ?

Flashcard 39: Determine the derivative of the function $y = \frac{2}{x^2}$ .

Flashcard 41: What is the derivative of $h(x) = 5x^3 - 4x + 8$ ?

Flashcard 42: What is the derivative of the function $g(x) = \frac{1}{x^4}$ ?

Flashcard 43: What is the derivative of $f(x) = 2x^3 - x^2 + 3$ ?

Flashcard 44: Find the derivative of $y = 2x^3 + 3x^2 - 5x + 1$ .

Flashcard 45: Determine the derivative of $g(x) = x^2 - \frac{1}{x}$ .

Flashcard 46: What is the derivative of $h(x) = 5x^3 - 4x + 8$ ?

Flashcard 47: Identify the derivative of $y = 3x^3 + 5x^2 - x$ .

Flashcard 49: What is the derivative of $h(x) = \frac{1}{x^5}$ ?

Flashcard 50: What is the derivative of the function $g(x) = x^4 - \frac{1}{x^2}$ ?

Flashcard 51: What is the derivative of the function $g(x) = x^4 - \frac{1}{x^2}$ ?

Flashcard 53: Find the rate of change of the area of a square with side length $s$ .

Flashcard 56: What is the formula for the derivative of $y = \frac{1}{x^3}$ ?

Flashcard 57: What is the derivative of $g(x) = x^3 + \frac{1}{x}$ ?

Flashcard 58: Determine the derivative of $f(x) = \frac{3}{x}$ .

Flashcard 59: What is the derivative of the function $h(x) = \frac{2}{x^3}$ ?

Flashcard 60: Identify the derivative of $y = \frac{1}{x} + x^2$ .

Flashcard 61: What is the derivative of $h(x) = \frac{1}{x^2}$ ?

Flashcard 62: Determine the derivative of $g(x) = x^2 - \frac{1}{x}$ .

Flashcard 64: Identify the derivative of the function $g(x) = \frac{1}{x}$ .

Flashcard 65: What is the derivative of $f(x) = x^3 - 2x + 4$ with respect to $x$ ?

Flashcard 66: What is the derivative of the function $f(x) = x^5 - 4x^3 + 2$ ?

Flashcard 68: Identify the derivative of $y = 6x^2 + 4x - 5$ .

Flashcard 70: Determine the derivative of the function $f(x) = 5x^4 - 3x^2 + 7$ .

Flashcard 72: What is the derivative of $f(x) = x^4 + 2x^2 + 1$ ?

Flashcard 73: Find the derivative of $y = 4x^4 - 3x^3 + x - 7$ .

Flashcard 74: What is the derivative of $g(x) = x^3 + \frac{1}{x}$ ?

Flashcard 75: Determine the derivative of the function $f(x) = 5x^4 - 3x^2 + 7$ .