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Calculus 1 : Differential Functions

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Example Questions

Example Question #851 : Other Differential Functions

Find the derivative.

-4x^3

Possible Answers:

-4x^2

-12x^2

12x^2

4x^3

Correct answer:

-12x^2

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying this rule to the function in the problem results in the following.

$\frac{d}{dx}(-4x^3)=3(-4)x^{3-1}=-12x^2$

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Example Question #852 : Other Differential Functions

Find the derivative.

4x-3

Possible Answers:

-4x

Correct answer:

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying this rule to each term of the function results in the following.

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

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

Thus, the derivative is 4.

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Example Question #1043 : Functions

What is the equation for the slope of the tangent line to:

8x^2-4x+4

Possible Answers:

8x+4

16x-4

16x+4

8x-4

Correct answer:

16x-4

Explanation:

To find the equation for the slope of the tangent line, find the derivative.

To find the derivative, use the power rule.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in,

$\frac{d}{dx}8x^2=16x$

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

$\frac{d}{dx}4=0$ .

Thus, the derivative is 16x-4 .

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Example Question #1044 : Functions

Find the derivative when x=3 .

x^3+5x^2

Possible Answers:

Correct answer:

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term within the function results in the following.

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

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

Thus, the derivative is 3x^2+10x

Now, substitute for .

3(3^2)+10(3)=57

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Example Question #857 : How To Find Differential Functions

Find the derivative when x=2 .

5x^2-3x

Possible Answers:

Correct answer:

Explanation:

First, use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in the following.

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

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

Thus, the derivative is 10x-3 .

Now, substitute 2 for x.

10(2)-3=17 .

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Example Question #1045 : Functions

Find the derivative.

$2x\cos (x)$

Possible Answers:

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

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

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

$2x\sin(x) +2\cos (x)$

Correct answer:

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

Explanation:

Use the product rule to find the derivative.

The product rule states,

$\frac{d}{dx}f(x)g(x)=f(x)g'(x)+g(x)f'(x)$ .

Given,

f(x)=2x

g(x)=cos(x)

and recalling the trigonometry derivative for cosine is,

$\frac{d}{dx}cos(x)=-sin(x)$

the derivatives are as follows.

$f'(x)=1\cdot 2x^{1-1}=2$

g'(x)=-sin(x)

Therefore, using the product rule the derivative becomes,

$2x(-\sin x)+2\cos (x)$ .

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Example Question #859 : How To Find Differential Functions

Find the derivative.

2x^4-x^3

Possible Answers:

8x^3+x^2

8x^3-x^2

8x^3+3x^2

8x^3-3x^2

Correct answer:

8x^3-3x^2

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in the following.

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

$\frac{d}{dx}(-x^3)=-3x^2$ .

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

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Example Question #861 : How To Find Differential Functions

Find the derivative.

$5x\sin (x)$

Possible Answers:

$5x\cos (x)+5\sin (x)$

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

$5x\cos (x)-\sin (x)$

$5x\cos (x)-5\sin (x)$

Correct answer:

$5x\cos (x)+5\sin (x)$

Explanation:

Use the product rule to find the derivative.

The product rule states,

$\frac{d}{dx}f(x)g(x)=f(x)g'(x)+g(x)f'(x)$ .

Given,

f(x)=5x

g(x)=sin(x)

and recalling the trigonometry derivative for sine is,

$\frac{d}{dx}sin(x)=cos(x)$

the derivative becomes,

$5x\cos (x)+5\sin (x)$ .

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Example Question #862 : How To Find Differential Functions

Find the derivative at x=6 .

4x^2

Possible Answers:

Correct answer:

Explanation:

First, find the derivative using the power rule.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule results in the following.

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

Now, substitute 6 for x.

8(6)=48 .

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Example Question #863 : How To Find Differential Functions

Find the derivative.

9x^2+7x-8

Possible Answers:

9x^2-7x

18x+7

18x-7

9x^2+7x

Correct answer:

18x+7

Explanation:

Use the power rule to find the derivative.

The power rule states,

$\frac{d}{dx}x^n=nx^{n-1}$ .

Applying the power rule to each term in the function results in the following.

$\frac{d}{dx}9x^2=18x$

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

$\frac{d}{dx}(-8)=0$

Thus, the derivative is 18x+7 .

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Calculus 1 : Differential Functions

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #851 : Other Differential Functions

Example Question #852 : Other Differential Functions

Example Question #1043 : Functions

Example Question #1044 : Functions

Example Question #857 : How To Find Differential Functions

Example Question #1045 : Functions

Example Question #859 : How To Find Differential Functions

Example Question #861 : How To Find Differential Functions

Example Question #862 : How To Find Differential Functions

Example Question #863 : How To Find Differential Functions

All Calculus 1 Resources

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