# Thread: And another derivative problem

1. ## And another derivative problem

y = 1/x^2

Find the derivative using lim f(x+h) - f(x) all divided by h

I worked it out and got -1/x^4

Can someone show how to do this

2. $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$

= $\displaystyle \lim_{h\to0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

= $\displaystyle \lim_{h\to0}\frac{x^2-(x+h)^2}{(x+h)^2x^2h}$

= $\displaystyle \lim_{h\to0}\frac{x^2-(x^2+2h+h^2)}{(x+h)^2x^2h}$

= $\displaystyle \lim_{h\to0}\frac{-2h-h^2}{(x+h)^2x^2h}$

= $\displaystyle \lim_{h\to0}\frac{-2-h}{(x+h)^2x^2}$

= $\displaystyle \frac{-2}{x^3}$

3. Yeah i know the formula...I had it in my post.

I can't get the right answer using that formula

4. Originally Posted by jzellt
Yeah i know the formula...I had it in my post.

I can't get the right answer using that formula
If you have done work, you should post it and say where you get stuck. Then a reply that is specific to your trouble can be written. Otherwise, someone will post the first few steps, only for you to say exactly what you said. This wastes everyone's time.