Chapter 2.3, Problem 26ES

Approximate $f^{\prime }\left(1\right)$ by considering the difference quotient

$\frac{f\left(1+h\right)-f\left(1\right)}{h}$

for values of $h$ near $0$ , and then find the exact value of $f^{\prime }\left(1\right)$ by

$f\left(x\right)=\frac{1}{x^2}$