\( f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}\)
\( \lim\limits_{h \to 0}\dfrac{\dfrac{1}{(x+h)^2}-\dfrac{1}{x^2}}{h}\)
\( \lim\limits_{h \to 0}\dfrac{1}{h}[\dfrac{x^2-(x+h)^2}{x^2(x+h)^2}]\)
\( \lim\limits_{h \to 0}\dfrac{1}{h}[\dfrac{x^2-x^2-2hx-h^2}{x^2(x+h)^2}]\)
\( \lim\limits_{h \to 0}\dfrac{1}{h}[\dfrac{-h^2-2hx}{x^2(x+h)^2}]\)
\( \lim\limits_{h \to 0}[\dfrac{-h^2-2hx}{x^2(x+h)^2}]\)
\( \dfrac{0-2x}{x^2(x+0)^2}=\dfrac{-2}{x^3}\)
Answered by Abhisek | 1 year ago