Question

d/dX(1)= value entha??​

Answer 1

Answer:

If you can't do the problem from the basic definitions, then you should know how... Here's the answer in complete detail:

Let f(x)=1xf(x)=1x.

Then for x≠0x≠0 and for −|x|<h<|x|−|x|<h<|x| with h≠0h≠0(which ensures that everything that follows is actually defined):

f(x+h)−f(x)=1x+h−1x=f(x+h)−f(x)=1x+h−1x= x−(x+h)x(x+h)=−hx(x+h)x−(x+h)x(x+h)=−hx(x+h)

So:

f(x+h)−f(x)h=−1x(x+h)f(x+h)−f(x)h=−1x(x+h).

So:

limh→0f(x+h)−f(x)h=limh→0−1x(x+h)=−1x2limh→0f(x+h)−f(x)h=limh→0−1x(x+h)=−1x2

So:

ddxf(x)=−1x2ddxf(x)=−1x2

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