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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 using the definition of derivative. State the domain of the function and the domain of its derivative.

f(x) = x4

To determine

To find: The derivative of the function f(x)=x4 and state the domain of the function and its derivative.

Explanation

Formula used:

The derivative of a function f, denoted by f(x), is

f(x)=limh0f(x+h)f(x)h (1)

Calculation:

Obtain the derivative of the function f(x).

Compute f(x) by using equation (1) as follows.

f(x)=limh0f(x+h)f(x)h=limh0(x+h)4x4h=limh0(x4+4x3h+6x2h2+4xh3+h4)x4h=limh0x4+4x3h+6x2h2+4xh3+h4x4h

Simplify the numerator,

f(x)=limh04x3h+6x2h2+4xh3+h4h=limh0h(4x3

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