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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the derivative of the function.

f ( x ) = 5 x + 1

To determine

To find: The derivative of f(x)=5x+1.

Explanation

Given:

The function is f(x)=5x+1.

Derivative rule: The Power Rule combined with the Chain Rule

If n is any real number and g(x) is differentiable function, then

ddx[g(x)]n=n[g(x)]n1g(x) (1)

Calculation:

Obtain the derivative of f(x).

f(x)=ddx(f(x))=ddx(5x+1)=ddx((5x+1)12)

Here, g(x)=5x+1.

Apply the Power Rule combined with the chain rule as shown in equation (1),

f(x)=ddx(5x+1)12=12(5x+1)121ddx<

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