calculus - finding a derivative with a limit?

Question

if f(x)=1/x, find the derivative WITH THE LIMIT! use the formula: [f(x+h)-f(x)]/h i know the answer (-1/x^2), i just need someone to show me the work cause i can't get it to work. thanks

i know i need to plug it in. can somebody show me the steps

Answer 1

Plug in your variables:
[h→0]lim (1/(x+h) - 1/x)/h
Obtain a common denominator:
[h→0]lim (x/(x(x+h)) - (x+h)/(x(x+h)))/h
Add like fractions:
[h→0]lim ((x-(x+h))/(x(x+h)))/h
Cancel the x's:
[h→0]lim (-h/(x(x+h)))/h
Cancel the h's:
[h→0]lim -1/(x(x+h))
Since h→0, the h term disappears, so:
-1/(x(x))
Which is:
-1/x²

Answer 2

All you have to do is plug in the value of f(x) into the long formula given to you. The answer should be the same as you specified before.

Answer 3

just plug them in.

so it would b lim(as h approches 0) of [f(x+h)-f(x)]/h

U NEED to SPECIFY A POINT WHERE U WANT THE DERIVITIVE