Question

Find the derivative of the following function from first principle:
$-x$

Answer 1

Let $f\left(x\right)=-x$
Thus using first principle
$f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}$
$=\underset{h\to 0}{lim}\frac{-(x+h)-(-x)}{h}$
$=\underset{h\to 0}{lim}\frac{-h}{h}=-1$