   Chapter 2.7, Problem 34E

Chapter
Section
Textbook Problem

Find f'(a).f(x) = x–2

To determine

To find: The derivative of the function f(x)=x2 at x=a.

Explanation

Formula used:

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

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

Calculation:

Obtain the derivative of the function f(x) at x=a.

Rewrite the function f(x) as follows.

f(x)=x2=1x2

Use the equation (1) to compute f(a).

f(a)=limh0f(a+h)f(a)h=limh0(1(a+h)2)(1a2)h=limh0(a2(a+h)2a2(a+h)2)h=limh0(a2(a2+h2+2ah))ha2(a+h)

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