AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

Study Derivative Rules Of Constant Sum Difference 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

Derivative Rules Of Constant Sum Difference

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QUESTION

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What is the derivative of $cf(x)$ , where $c$ is a constant?

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ANSWER

$(cf)' = cf'$ . Constant multiple rule: factor out the constant.

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What this deck covers

This deck focuses on Derivative Rules Of Constant Sum Difference, 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.

All flashcards

Flashcard 1: What is the derivative of $cf(x)$ , where $c$ is a constant?

Answer: $(cf)' = cf'$ . Constant multiple rule: factor out the constant.

Flashcard 2: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 3: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Answer: $(f + g)' = f' + g'$ . Derivative of sum equals sum of derivatives.

Flashcard 4: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Answer: $f'(x)+g'(x)$ . Differentiate each term separately and add.

Flashcard 5: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Answer: $3f'(x)-2g'(x)$ . Apply constant multiple rule to each term.

Flashcard 6: What is $rac{d}{dx}[5f(x)]$ ?

Answer: $5f'(x)$ . Apply constant multiple rule: pull out 5.

Flashcard 7: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 8: What is $rac{d}{dx}[-4f(x)+g(x)]$ ?

Answer: $-4f'(x)+g'(x)$ . Apply constant multiple rule to each term.

Flashcard 9: What is $rac{d}{dx}[7-f(x)-g(x)]$ ?

Answer: $-f'(x)-g'(x)$ . Constant 7 has derivative 0; negative signs carry through.

Flashcard 10: Calculate the derivative of $5x - 3$ .

Answer:

Derivative of linear function is the coefficient of $x$ .

Flashcard 11: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 12: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Answer: $(f + g)' = f' + g'$ . Derivative of sum equals sum of derivatives.

Flashcard 13: What is $rac{d}{dx}[-2g(x)]$ ?

Answer: $-2g'(x)$ . Apply constant multiple rule: pull out -2.

Flashcard 14: State the derivative of the function $-5$ .

Answer:

Any constant has derivative zero.

Flashcard 15: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Answer:

Constant multiple rule: derivative of $cx$ is $c$ .

Flashcard 16: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 17: What is $rac{d}{dx}[ rac{1}{2}f(x)+ rac{3}{2}g(x)]$ ?

Answer: $rac{1}{2}f'(x)+ rac{3}{2}g'(x)$ . Fractional constants follow the same rule.

Flashcard 18: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?

Answer: $0$ . The derivative of any constant is zero.

Flashcard 19: What is $rac{d}{dx}[7]$ ?

Answer: $0$ . 7 is a constant, so its derivative is 0.

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Answer: $-g'(x)$ . Derivative of 12 is 0; $-g(x)$ gives $-g'(x)$ .

Flashcard 21: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 22: What is $rac{d}{dx}[-3]$ ?

Answer: $0$ . -3 is a constant, so its derivative is 0.

Flashcard 23: Calculate the derivative of $5x - 3$ .

Answer: $5$ . Derivative of linear function is the coefficient of $x$ .

Flashcard 24: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Answer: $f'(x)-g'(x)$ . Differentiate each term separately and subtract.

Flashcard 25: What is $rac{d}{dx}[f(x)+9]$ ?

Answer: $f'(x)$ . Derivative of constant 9 is 0, leaving $f'(x)$ .

Flashcard 26: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Answer: $(f - g)' = f' - g'$ . Derivative of difference equals difference of derivatives.

Flashcard 27: Calculate the derivative of $12x$ .

Answer:

Derivative of linear term $12x$ is the coefficient.

Flashcard 28: State the derivative of $x^n$ where $n$ is a constant.

Answer: $nx^{n-1}$ . Power rule: bring down exponent, reduce by 1.

Flashcard 29: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 30: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Answer: $2f'(x)+3g'(x)$ . Constant -5 has derivative 0; apply rules to rest.

Flashcard 31: State the derivative of $x^n$ where $n$ is a constant.

Answer: $nx^{n-1}$ . Power rule: bring down exponent, reduce by 1.

Flashcard 32: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Answer: $f'(x)-g'(x)+h'(x)$ . Apply sum/difference rules term by term.

Flashcard 33: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 34: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Answer: $f'(x)+g'(x)+h'(x)$ . Sum rule extends to any number of functions.

Flashcard 35: Calculate the derivative of $12x$ .

Answer:

Derivative of linear term $12x$ is the coefficient.

Flashcard 36: State the derivative of the function $-5$ .

Answer:

Any constant has derivative zero.

Flashcard 37: What is the derivative of $cf(x)$ , where $c$ is a constant?

Answer: $(cf)' = cf'$ . Constant multiple rule: factor out the constant.

Flashcard 38: Find and correct the derivative: $rac{d}{dx}[f(x)+g(x)]=f'(x)g'(x)$ .

Answer: Correct: $rac{d}{dx}[f(x)+g(x)]=f'(x)+g'(x)$ . Sum rule gives addition, not multiplication of derivatives.

Flashcard 39: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Answer: $(f - g)' = f' - g'$ . Derivative of difference equals difference of derivatives.

Flashcard 40: What is $rac{d}{dx}[- rac{5}{3}f(x)- rac{1}{3}]$ ?

Answer: $- rac{5}{3}f'(x)$ . Constant $- rac{1}{3}$ has derivative 0.

Flashcard 41: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 42: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Answer: $c ext{ }f'(x)$ . Pull out the constant and multiply by the derivative.

Flashcard 43: Find and correct the derivative: $rac{d}{dx}[3f(x)]=3f(x)$ .

Answer: Correct: $rac{d}{dx}[3f(x)]=3f'(x)$ . Must differentiate $f(x)$ , not just copy it.

Flashcard 44: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Answer:

Constant multiple rule: derivative of $cx$ is $c$ .

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

Derivative Rules Of Constant Sum Difference

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What is the derivative of cf(x)cf(x)cf(x), where ccc is a constant?

Flashcard 2: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 3: State the derivative rule for the sum of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 4: State the sum rule: What is rac{d}{dx}[f(x)+g(x)]?

Flashcard 5: What is rac{d}{dx}[3f(x)-2g(x)]?

Flashcard 6: What is rac{d}{dx}[5f(x)]?

Flashcard 7: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 8: What is rac{d}{dx}[-4f(x)+g(x)]?

Flashcard 9: What is rac{d}{dx}[7-f(x)-g(x)]?

Flashcard 10: Calculate the derivative of 5x−35x - 35x−3.

Flashcard 11: What is the derivative of a constant ccc with respect to xxx?

Flashcard 12: State the derivative rule for the sum of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 13: What is rac{d}{dx}[-2g(x)]?

Flashcard 14: State the derivative of the function −5-5−5.

Flashcard 15: What is the derivative of a constant multiplied by xxx, 7x7x7x?

Flashcard 16: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 17: What is rac{d}{dx}[ rac{1}{2}f(x)+ rac{3}{2}g(x)]?

Flashcard 18: State the constant rule: What is rac{d}{dx}[c] for a constant ccc?

Flashcard 19: What is rac{d}{dx}[7]?

Flashcard 20: What is rac{d}{dx}[12-g(x)]?

Flashcard 21: Find the derivative of 8x−28x - 28x−2.

Flashcard 22: What is rac{d}{dx}[-3]?

Flashcard 23: Calculate the derivative of 5x−35x - 35x−3.

Flashcard 24: State the difference rule: What is rac{d}{dx}[f(x)-g(x)]?

Flashcard 25: What is rac{d}{dx}[f(x)+9]?

Flashcard 26: State the derivative rule for the difference of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 27: Calculate the derivative of 12x12x12x.

Flashcard 28: State the derivative of xnx^nxn where nnn is a constant.

Flashcard 29: What is the derivative of a constant ccc with respect to xxx?

Flashcard 30: What is rac{d}{dx}[2f(x)+3g(x)-5]?

Flashcard 31: State the derivative of xnx^nxn where nnn is a constant.

Flashcard 32: What is rac{d}{dx}[f(x)-g(x)+h(x)]?

Flashcard 33: Find the derivative of 8x−28x - 28x−2.

Flashcard 34: What is rac{d}{dx}[f(x)+g(x)+h(x)]?

Flashcard 35: Calculate the derivative of 12x12x12x.

Flashcard 36: State the derivative of the function −5-5−5.

Flashcard 37: What is the derivative of cf(x)cf(x)cf(x), where ccc is a constant?

Flashcard 38: Find and correct the derivative: rac{d}{dx}[f(x)+g(x)]=f'(x)g'(x).

Flashcard 39: State the derivative rule for the difference of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 40: What is rac{d}{dx}[- rac{5}{3}f(x)- rac{1}{3}]?

Flashcard 41: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 42: State the constant multiple rule: What is rac{d}{dx}[c ext{ }f(x)] for constant ccc?

Flashcard 43: Find and correct the derivative: rac{d}{dx}[3f(x)]=3f(x).

Flashcard 44: What is the derivative of a constant multiplied by xxx, 7x7x7x?

Flashcard 1: What is the derivative of $cf(x)$ , where $c$ is a constant?

Flashcard 2: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 3: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Flashcard 4: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Flashcard 5: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Flashcard 6: What is $rac{d}{dx}[5f(x)]$ ?

Flashcard 7: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 8: What is $rac{d}{dx}[-4f(x)+g(x)]$ ?

Flashcard 9: What is $rac{d}{dx}[7-f(x)-g(x)]$ ?

Flashcard 10: Calculate the derivative of $5x - 3$ .

Flashcard 11: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 12: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Flashcard 13: What is $rac{d}{dx}[-2g(x)]$ ?

Flashcard 14: State the derivative of the function $-5$ .

Flashcard 15: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Flashcard 16: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 17: What is $rac{d}{dx}[ rac{1}{2}f(x)+ rac{3}{2}g(x)]$ ?

Flashcard 18: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?

Flashcard 19: What is $rac{d}{dx}[7]$ ?

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Flashcard 21: Find the derivative of $8x - 2$ .

Flashcard 22: What is $rac{d}{dx}[-3]$ ?

Flashcard 23: Calculate the derivative of $5x - 3$ .

Flashcard 24: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Flashcard 25: What is $rac{d}{dx}[f(x)+9]$ ?

Flashcard 26: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Flashcard 27: Calculate the derivative of $12x$ .

Flashcard 28: State the derivative of $x^n$ where $n$ is a constant.

Flashcard 29: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 30: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Flashcard 31: State the derivative of $x^n$ where $n$ is a constant.

Flashcard 32: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Flashcard 33: Find the derivative of $8x - 2$ .

Flashcard 34: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Flashcard 35: Calculate the derivative of $12x$ .

Flashcard 36: State the derivative of the function $-5$ .

Flashcard 37: What is the derivative of $cf(x)$ , where $c$ is a constant?

Flashcard 38: Find and correct the derivative: $rac{d}{dx}[f(x)+g(x)]=f'(x)g'(x)$ .

Flashcard 39: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Flashcard 40: What is $rac{d}{dx}[- rac{5}{3}f(x)- rac{1}{3}]$ ?

Flashcard 41: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 42: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Flashcard 43: Find and correct the derivative: $rac{d}{dx}[3f(x)]=3f(x)$ .

Flashcard 44: What is the derivative of a constant multiplied by $x$ , $7x$ ?