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Calculus 1 : Functions

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Example Questions

Example Question #951 : Functions

Find the derivative.

(2x^2-4)(4x^3)

Possible Answers:

40x^4-48x^2

40x^4+48x^2

8x^4-48x^2

-40x^4-48x^2

Correct answer:

40x^4-48x^2

Explanation:

Use the product rule to find this derivative.

(2x^2-4)(12x^2)+(4x^3)(4x)=24x^4-48x^2+16x^4=40x^4-48x^2

Thus, the derivative is 40x^4-48x^2

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Example Question #952 : Functions

Find the derivative.

$\frac{3}{x^3}$

Possible Answers:

$\frac{-9}{x^4}$

$\frac{3}{x^4}$

$\frac{9}{x^4}$

$\frac{-3}{x^4}$

Correct answer:

$\frac{-9}{x^4}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{(x^3)(0)-3(3x^2)}{(x^3)^2}=\frac{-9x^2}{x^6}=\frac{-9}{x^4}$

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Example Question #765 : How To Find Differential Functions

Find the derivative.

x^3+4x^2+7x

Possible Answers:

3x^2+8x+7

3x^2+8x

3x^3+8x^2+7x

3x^2-8x-7

Correct answer:

3x^2+8x+7

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}x^3=3x^2$

$\frac{d}{dx}4x^2=8x$

$\frac{d}{dx}7x=7$

Thus, the derivative is 3x^2+8x+7 .

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Example Question #953 : Functions

Find the derivative.

$\frac{7}{x^4}$

Possible Answers:

$\frac{28}{x^5}$

$\frac{-28}{x^5}$

$\frac{-14}{x^5}$

$\frac{-28}{x^4}$

Correct answer:

$\frac{-28}{x^5}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{x^4(0)-7(4x^3)}{(x^4)^2}=\frac{-28x^3}{x^8}$

Simplify.

The derivative is $\frac{-28}{x^5}$ .

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Example Question #954 : Functions

Find the derivative.

$\frac{x}{2}$

Possible Answers:

$\frac{x}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{2(1)-x(0)}{(2)^2}=\frac{2}{4}=\frac{1}{2}$

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Example Question #955 : Differential Functions

Find the derivative.

x^3+2x^4-x^2

Possible Answers:

-8x^3+3x^2-2x

8x^3+3x^2-2x

8x^3-3x^2-2x

8x^3+3x^2+2x

Correct answer:

8x^3+3x^2-2x

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}x^3=3x^2$

$\frac{d}{dx}2x^4=8x^3$

$\frac{d}{dx}-x^2=-2x$

Thus, the derivative is 8x^3+3x^2-2x .

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Example Question #955 : Functions

Find the derivative.

2x^2(3x^2-4x)

Possible Answers:

24x^3+12x^2

24x^3-24x^2

24x^3+24x^2

12x^3-24x^2

Correct answer:

24x^3-24x^2

Explanation:

Use the product rule to find this derivative.

2x^2(6x-4)+(4x)(3x^2-4x)=12x^3-8x^2+12x^3-16x^2=24x^3-24x^2

Thus, the derivative is 24x^3-24x^2 .

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Example Question #956 : Functions

Find the derivative.

$\frac{6}{x^3}$

Possible Answers:

$\frac{12}{x^3}$

$\frac{18}{x^4}$

$\frac{12}{x^4}$

$\frac{18}{x^3}$

Correct answer:

$\frac{18}{x^4}$

Explanation:

Use the quotient rule.

$\frac{x^3(0)-6(3x^2)}{(x^3)^2}=\frac{18x^2}{x^6}=\frac{18}{x^4}$

The derivative is $\frac{18}{x^4}$ .

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Example Question #957 : Functions

Find the derivative.

$\frac{9}{x^4}$

Possible Answers:

$\frac{-36}{x^4}$

$\frac{-36}{x^5}$

$\frac{36}{x^4}$

$\frac{36}{x^5}$

Correct answer:

$\frac{-36}{x^5}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{x^4(0)-9(4x^3)}{(x^4)^2}=\frac{-36x^3}{x^8}=\frac{-36}{x^5}$

Thus, the derivative is $\frac{-36}{x^5}$ .

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Example Question #958 : Functions

Find the derivative.

6x^2(3x^2+8x)

Possible Answers:

72x^3+144

72x^3-144x^2

72x^3+144x^2

72x^3+144x

Correct answer:

72x^3+144x^2

Explanation:

Use the product rule to find the derivative.

6x^2(6x+8)+(3x^2+8x)12x=36x^3+48x^2+36x^3+96x^2

Simplify, and the derivative is 72x^3+144x^2 .

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Calculus 1 : Functions

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #951 : Functions

Example Question #952 : Functions

Example Question #765 : How To Find Differential Functions

Example Question #953 : Functions

Example Question #954 : Functions

Example Question #955 : Differential Functions

Example Question #955 : Functions

Example Question #956 : Functions

Example Question #957 : Functions

Example Question #958 : Functions

All Calculus 1 Resources

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