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Calculus 1 : Calculus

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Example Questions

Example Question #1971 : Calculus

Find the derivative.

x^6-x^2+x^4

Possible Answers:

6x^4+4x^2-2x

6x^5+4x^3-2x

6x^5+4x^3-2

x^5+x^3-x

Correct answer:

6x^5+4x^3-2x

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}x^6=6x^5$

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

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

Thus, the derivative is 6x^5+4x^3-2x .

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Example Question #1972 : Calculus

Find the derivative.

$\frac{2}{y^4}$

Possible Answers:

$\frac{-8}{y^4}$

$\frac{8}{y^4}$

$\frac{-8}{y^5}$

$\frac{8}{y^5}$

Correct answer:

$\frac{-8}{y^5}$

Explanation:

Use the quotient rule to find the derivative.

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

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Example Question #1973 : Calculus

Find the derivative.

3x^2-3x+3

Possible Answers:

6x-3

6x^2-3x

3x-1

Correct answer:

6x-3

Explanation:

Use the power rule to find the derivative.

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

$\frac{d}{dx}-3x=-3$

Recall that the derivative of a constant is zero.

Thus, the derivative is 6x-3 .

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Example Question #1974 : Calculus

Find the derivative.

$\frac{8}{x}$

Possible Answers:

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

$\frac{-8}{x^2}$

$\frac{8}{x^2}$

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

Correct answer:

$\frac{-8}{x^2}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{x(0)-8(1)}{(x)^2}=\frac{-8}{x^2}$ .

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Example Question #1975 : Calculus

Find the derivative.

4(x^7+2x^3)

Possible Answers:

7x^6+6x^2

28x^6+24x^2

Correct answer:

28x^6+24x^2

Explanation:

Begin by distributing the 4 throughout.

4x^7+8x^3

Now, use the power rule to find the derivative.

$\frac{d}{dx}4x^7=28x^6$

$\frac{d}{dx}8x^3=24x^2$

Thus, the derivative is 28x^6+24x^2

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Example Question #1976 : Calculus

Find the derivative.

5x^2+3x+6

Possible Answers:

5x+3

10x^2+3x+6

10x+3

Correct answer:

10x+3

Explanation:

Use the power rule to find this derivative.

$\frac{d}{dx}5x^2=10x$

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

Recall that the derivative of a constant is zero.

Thus, the derivative is 10x+3 .

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Example Question #1977 : Calculus

Find the derivative.

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Use the quotient rule to find this derivative.

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

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Example Question #1978 : Calculus

Find the derivative.

3x^3(2x-1)

Possible Answers:

18x^3-9x^2

24x^3-9x^2

6x^4+18x^3-9x^2

18x^3-9x^2

Correct answer:

24x^3-9x^2

Explanation:

Use the product rule to find this derivative.

3x^3(2)+(2x-1)9x^2=6x^3+18x^3-9x^2

Thus, the derivative is 24x^3-9x^2 .

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Example Question #1979 : Calculus

Find the derivative.

x^4+2x^2-7x

Possible Answers:

4x^3-4x-7

-4x^3+4x-7

4x^3+4x-7

4x^3+4x+7

Correct answer:

4x^3+4x-7

Explanation:

Use the power rule to find this derivative.

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

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

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

Thus, the derivative is 4x^3+4x-7

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Example Question #1980 : Calculus

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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Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #1971 : Calculus

Example Question #1972 : Calculus

Example Question #1973 : Calculus

Example Question #1974 : Calculus

Example Question #1975 : Calculus

Example Question #1976 : Calculus

Example Question #1977 : Calculus

Example Question #1978 : Calculus

Example Question #1979 : Calculus

Example Question #1980 : Calculus

All Calculus 1 Resources

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