Answer
(a) $\frac{1}{(x+h)^2}$
(b) $\frac{-2xh-h^2}{x^2(x+h)^2}$
(c) $\frac{-2x-h}{x^2(x+h)^2}$
Work Step by Step
(a) Given $f(x)=\frac{1}{x^2}$, we have $f(x+h)=\frac{1}{(x+h)^2}$
(b) $f(x+h)-f(x)=\frac{1}{(x+h)^2}-\frac{1}{x^2}=\frac{x^2-(x+h)^2}{x^2(x+h)^2}=\frac{-2xh-h^2}{x^2(x+h)^2}$
(c) $\frac{f(x+h)-f(x)}{h}=\frac{-2x-h}{x^2(x+h)^2}$
