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Chapter 2: Q. 52 (page 184)

Use the definition of the derivative to find ffor each function fin Exercises 39-54

f(x)=1x2-1

Short Answer

Expert verified

The derivative isf'(x)=-1x2-12

Step by step solution

01

Given information

Given functionf(x)=1x2-1

02

Use the rule to calculate the derivative

Calculating, we get

f(x)=1x2-1f'(x)=(x2-1)-1f'(x)=-(x2-1)-1-1f'(x)=-(x2-1)-2f'(x)=-1(x2-1)2

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Most popular questions from this chapter

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

After t=2 seconds, with h=0.1,h=0.01h=-0.1andh=-0.01

Use the definition of the derivative to find f'for each function fin Exercises39-54

f(x)=21-x

A bowling ball dropped from a height of 400feet will be s(t)=400-16t2feet from the ground after tseconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:

When the bowling ball hits the ground, withh=-0.5,h=-0.2andh=-0.1

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

26.f(x)=1x2,x=2

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x-12(x2-1)3

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