Question

Find the derivative by the limit process? f(x)=1/x^2 I would appreciate if someone helped me.?

Answer 1

\[\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\]
\[= \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}\]
\[= \frac{x^2 - (x+h)^2}{h [x^2 (x+h)^2]}\]
\[= \frac{x^2 - (x^2 +2xh +h^2)}{h [x^2 (x+h)^2]}\]
\[= \frac{h (-2x-h)}{h [x^2 (x+h)^2]}\]
\[\rightarrow \lim_{h \rightarrow 0} \frac{-2x -h}{x^2 (x+h)^2} = \frac{-2x}{x^4} = \frac{-2}{x^3}\]

Answer 2

that is solution, hope you can follow the steps