Differentiate each of the following from first principle: `(-x)^(-1)`

Explanation

`f'(x)=lim_(h->0)frac{f(x+h)-f(x)}{h}`

`=lim_(h->0)frac{-frac{1}{x+h}+frac{1}{x}}{h}`

`=lim_(h->0)frac{-x+(x+h)}{x(x+h)h}`

`=lim_(h->0)frac{h}{hx(x+h)}`

`=frac{1}{x^2}`