Answer
$-10$
Work Step by Step
To find the derivative of a function by the limit process, plug into the formula $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$:
$f'(x)=\lim\limits_{h \to 0}\frac{-10(x+h)-(-10x)}{h}$
Simplify:
$f'(x)=\lim\limits_{h \to 0}\frac{-10x-10h+10x}{h}$
$x$- and $h$-values will cancel themselves out:
$f'(x)=\lim\limits_{h \to 0}\frac{10h}{h}$
$f'(x)=-10$
