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Calculus 1 : How to find differential functions

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Example Questions

Example Question #311 : How To Find Differential Functions

Find the derivative.

$\frac{3}{5+x}$

Possible Answers:

$-\frac{3}{x^{2}+10x+25}$

$\frac{3}{x+5}$

$\frac{3}{x^{2}+10x+25}$

$-\frac{3}{x+5}$

Correct answer:

$-\frac{3}{x^{2}+10x+25}$

Explanation:

Use the quotient rule to find the derivative.

$\frac{(5+x)(0)-3(1)}{(5+x)^{2}}$

$-\frac{3}{(5+x)^{2}}=-\frac{3}{x^{2}+10x+25}$

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Example Question #312 : How To Find Differential Functions

Find the derivative.

$7x^{3}-3$

Possible Answers:

21x

21x-3

21x^2

14x^2

Correct answer:

21x^2

Explanation:

Find the derivative using the power rule.

$\frac{d}{dx}7x^3=21x^2$

$\frac{d}{dx}-3=0$

The derivative is $21x^{2}$ .

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Example Question #500 : Differential Functions

What is the slope of the tangent line at x=3 ?

3x+4

Possible Answers:

$\frac{3}{4}$

Correct answer:

Explanation:

In order to find the slope of the tangent line at x=3 , find the derivative of the function.

$\frac{d}{dx}(3x+4)=3$

Because the derivative is a constant, the slope of the tangent line is also constant: .

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Example Question #313 : Other Differential Functions

Find the slope of the tangent line at x=0 .

$x^{3}+3x^{2}-2x$

Possible Answers:

Correct answer:

Explanation:

Begin by finding the derivative using the power rule.

$3x^{2}+6x-2$

Now, substitute for .

$2(0^{2})+6(0)-2$

The answer is -2.

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Example Question #1531 : Calculus

Find the derivative.

$\cos(x)\sin (x)$

Possible Answers:

$\cos ^{2}(x)$

$\cos^2 (x)-\sin^2(x)$

$\cos (x)\sin (x)$

Correct answer:

$\cos^2 (x)-\sin^2(x)$

Explanation:

Use the product rule to find the derivative.

Recall that the derivative of $\sin$ is $\cos$ , and the derivative of $\cos$ is $-\sin$ .

$\cos (x)\cos (x)-\sin (x)\sin (x)$

Simplify.

$\cos^2 (x)-\sin^2(x)$

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Example Question #1532 : Calculus

Find the slope of the tangent line at x=8 .

$2x^{3}-x^{2}+3x$

Possible Answers:

402

371

330

365

Correct answer:

371

Explanation:

First, find the derivative by using the power rule.

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

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

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

Thus, the derivative is $6x^{2}-2x+3$ .

Now, substitute for .

6(8)^2-2(8)+3=371

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Example Question #1531 : Calculus

Find the derivative.

2x-5

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

Use the power rule to find the derivative.

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

$\frac{d}{dx}-5=0$

Thus, the derivative equals .

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Example Question #1534 : Calculus

Find the derivative at x=2.5 .

4x+17

Possible Answers:

Correct answer:

Explanation:

First, find the derivative using the power rule.

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

$\frac{d}{dx}17=0$

The derivative is , regardless of the value.

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Example Question #1535 : Calculus

Find the derivative at x=4 .

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

Possible Answers:

$-\frac{17}{256}$

$-\frac{13}{256}$

$-\frac{9}{256}$

$-\frac{1}{256}$

Correct answer:

$-\frac{9}{256}$

Explanation:

Use the quotient rule to find the derivative.

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

$-\frac{9x^{2}}{x^{6}}=-\frac{9}{x^{4}}$

Now, substitute 4 for x.

$-\frac{9}{4^4}=-\frac{9}{256}$

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Example Question #1532 : Calculus

Find the derivative.

9-3x

Possible Answers:

-3x

Correct answer:

Explanation:

Use the power rule to find the derivative.

$\frac{d}{dx}9=0$

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

The derivative is .

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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 #311 : How To Find Differential Functions

Example Question #312 : How To Find Differential Functions

Example Question #500 : Differential Functions

Example Question #313 : Other Differential Functions

Example Question #1531 : Calculus

Example Question #1532 : Calculus

Example Question #1531 : Calculus

Example Question #1534 : Calculus

Example Question #1535 : Calculus

Example Question #1532 : Calculus

All Calculus 1 Resources

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