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Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

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10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1991 : Calculus

Find the derivative.

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

Possible Answers:

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

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

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

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

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 #1992 : Calculus

Find the derivative.

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

Possible Answers:

240x^4-120x^2

240x^4+120x^2

40x^4-20x^2

40x^4+20x^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 #1993 : Calculus

Find the derivative.

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

Possible Answers:

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

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

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

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

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 #1994 : Calculus

Find the derivative.

5x^4+3x^2-10

Possible Answers:

20x^2+6x

10x^3+6x

20x^3+6x

10x^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 #1995 : Calculus

Find the derivative.

$\frac{9}{3x}$

Possible Answers:

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

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

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

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

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 #1996 : Calculus

Find the derivative.

5x^3-2x^2

Possible Answers:

5x^2-4x

15x^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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Example Question #1997 : Calculus

Find the derivative.

6x^2(4x^3+3x)

Possible Answers:

120x^4+32x^2

120x^4+52x^2

120x^3-52x^2

20x^4+52x^2

Correct answer:

120x^4+52x^2

Explanation:

Use the product rule to find the derivative.

6x^2(12x^2+3)+(4x^3+3x)12x=72x^4+18x^2+48x^4+36x^2

Combine like terms.

The derivative is 120x^4+52x^2 .

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Example Question #1998 : Calculus

Find the derivative.

$\frac{2}{3x^4}$

Possible Answers:

$\frac{-8}{3x^5}$

$\frac{8}{3x^8}$

$\frac{-8}{3x^8}$

$\frac{8}{3x^5}$

Correct answer:

$\frac{-8}{3x^5}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{3x^4(0)-2(12x^3)}{(3x^4)^2}=\frac{-24x^3}{9x^8}$

Simplify.

The derivative is $\frac{-8}{3x^5}$ .

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Example Question #1999 : Calculus

Find the derivative.

$\frac{1}{x^5}$

Possible Answers:

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

$\frac{5}{x^6}$

$\frac{-5}{x^6}$

$\frac{5}{x^6}$

Correct answer:

$\frac{-5}{x^6}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{x^5(0)-1(5x^4)}{(x^5)^2}=\frac{-5x^4}{x^{10}}=\frac{-5}{x^6}$

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Example Question #2000 : Calculus

Find the derivative.

$12x^{12}$

Possible Answers:

$-12x^{12}$

$144x^{12}$

$12x^{11}$

$144x^{11}$

Correct answer:

$144x^{11}$

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}12x^{12}=144x^{11}$

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Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #1991 : Calculus

Example Question #1992 : Calculus

Example Question #1993 : Calculus

Example Question #1994 : Calculus

Example Question #1995 : Calculus

Example Question #1996 : Calculus

Example Question #1997 : Calculus

Example Question #1998 : Calculus

Example Question #1999 : Calculus

Example Question #2000 : Calculus

All Calculus 1 Resources

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