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Chapter 2: Q 3. (page 237)

Find the derivatives off(x)=1x.

Short Answer

Expert verified

The derivative off(x)=1xis-1x2.

Step by step solution

01

Given Information 

The given expression isf(x)=1x.

02

Simplification  

f'(x)=limh鈫�0f(x+h)-f(x)hf'(1x)=limh鈫�0(1x+h)-1xh=limh鈫�0x-x-hx(x+h)脳h=limh鈫�0-h(x2+xh)脳h=-1x2+x.0=-1x2

Therefore, the derivate of1xis-1x2.

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Most popular questions from this chapter

Taking the limit: We have seen that if f is a smooth function, then f'(c)鈮�f(c+h)-f(c)hThis approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.

f'(c)=limh鈫�0f(c+h)-f(c)h.

Use the limit just defined to calculate the exact slope of the tangent line tof(x)=x2atx=4.

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