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Chapter 2: Q. 45 (page 184)

Use the definition of the derivative to find f'for each function fin Exercises 34-59

f(x)=1x2

Short Answer

Expert verified

The value off'(x)=-2x3

Step by step solution

01

Step 1. Given  information

The given functionf(x)=1x2

02

Step 2. Finding the value of f'(x)

We know that f'(x)=limh鈫�0f(x+h)-f(x)h.........(1)

Given f(x)=1x2the

Putting the values in (1)

localid="1648748944158" role="math" f'(x)=limh鈫�01(x+h)2-1x2h=limh鈫�0x2-(x+h)2x2(x+h)2h=limh鈫�0x2-x2-h2-2xhx2(x+h)2h=limh鈫�0-h2-2xhx2(x+h)2h=limh鈫�0h(-h-2x)x2(x+h)2h=limh鈫�0h(-h-2x)x2(x+h)2脳1h=limh鈫�0(-h-2x)x2(x+h)2

Putting h=0

=-(0)-2xx2.(x+0)2=-2xx2.x2=-2x3

Hence,the value off'(x)=-2x3

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Most popular questions from this chapter

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

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