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
$\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$
= $\displaystyle \lim_{h\to0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$
= $\displaystyle \lim_{h\to0}\frac{x^2-(x+h)^2}{(x+h)^2x^2h}$
= $\displaystyle \lim_{h\to0}\frac{x^2-(x^2+2h+h^2)}{(x+h)^2x^2h}$
= $\displaystyle \lim_{h\to0}\frac{-2h-h^2}{(x+h)^2x^2h}$
= $\displaystyle \lim_{h\to0}\frac{-2-h}{(x+h)^2x^2}$
= $\displaystyle \frac{-2}{x^3}$