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Calculus 1 : How to find differential functions

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Example Questions

Example Question #771 : How To Find Differential Functions

Find the derivative.

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

Possible Answers:

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

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

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

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

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 #772 : How To Find Differential Functions

Find the derivative.

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

Possible Answers:

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

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

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

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

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 #773 : How To Find Differential Functions

Find the derivative.

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

Possible Answers:

72x^3+144x

72x^3+144

72x^3-144x^2

72x^3+144x^2

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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Example Question #774 : How To Find Differential Functions

Find the derivative.

9x^3

Possible Answers:

9x^2

27x^2

18x^2

3x^2

Correct answer:

27x^2

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}9x^3=27x^2$

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Example Question #775 : How To Find Differential Functions

Find the derivative.

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Use the quotient rule to find the derivative.

$\frac{x^3(0)-4(3x^2)}{(x^3)^2}=\frac{-12x^2}{x^6}$

Simplify.

The derivative is $\frac{-12}{x^4}$ .

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Example Question #776 : How To Find Differential Functions

Find the derivative.

8x^2(6x^3-5x)

Possible Answers:

40x^4-20x^2

40x^4+20x^2

240x^4-120x^2

240x^4+120x^2

Correct answer:

240x^4-120x^2

Explanation:

Use the product rule to find the derivative.

8x^2(18x^2-5)+(6x^3-5x)16x=144x^4-40x^2+96x^4-80x^2=240x^4-120x^2

Thus, the derivative is 240x^4-120x^2 .

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Example Question #777 : How To Find Differential Functions

Find the derivative.

$\frac{7}{2x^3}$

Possible Answers:

$\frac{-21}{x^4}$

$\frac{-10}{x^4}$

$\frac{-21}{2x^4}$

$\frac{21}{2x^4}$

Correct answer:

$\frac{-21}{2x^4}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{2x^3(0)-7(6x^2)}{(2x^3)^2}=\frac{-42x^2}{4x^6}$

Simplify.

The derivative is $\frac{-21}{2x^4}$

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Example Question #778 : How To Find Differential Functions

Find the derivative.

5x^4+3x^2-10

Possible Answers:

10x^2+6x

10x^3+6x

20x^3+6x

20x^2+6x

Correct answer:

20x^3+6x

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}5x^4=20x^3$

$\frac{d}{dx}3x^2=6x$

Recall that the derivative of a constant is zero.

Thus, the derivative is 20x^3+6x .

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Example Question #779 : How To Find Differential Functions

Find the derivative.

$\frac{9}{3x}$

Possible Answers:

$\frac{-3}{x^2}$

$\frac{1}{x^2}$

$\frac{-1}{x^2}$

$\frac{3}{x^2}$

Correct answer:

$\frac{-3}{x^2}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{3x(0)-9(3)}{(3x)^2}=\frac{-27}{9x^2}$

Simplify.

The derivative is $\frac{-3}{x^2}$ .

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Example Question #780 : How To Find Differential Functions

Find the derivative.

5x^3-2x^2

Possible Answers:

15x^2+4x

5x^2-4x

15x^2-4

15x^2-4x

Correct answer:

15x^2-4x

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}5x^3=15x^2$

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

Thus, the derivative is 15x^2-4x .

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Calculus 1 : How to find differential functions

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #771 : How To Find Differential Functions

Example Question #772 : How To Find Differential Functions

Example Question #773 : How To Find Differential Functions

Example Question #774 : How To Find Differential Functions

Example Question #775 : How To Find Differential Functions

Example Question #776 : How To Find Differential Functions

Example Question #777 : How To Find Differential Functions

Example Question #778 : How To Find Differential Functions

Example Question #779 : How To Find Differential Functions

Example Question #780 : How To Find Differential Functions

All Calculus 1 Resources

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