Question

If $y=\frac{1}{x^{10}}=x^{-10}$, then find $\frac{dy}{dx}$.

Answer 1

Differentiating both sides w.r.t. $x$, using $\frac{d\left[x^n\right]}{dx}=n{x}^{n-1}$, we get
$\frac{dy}{dx}=\frac{d\left[x^{-10}\right]}{dx}=-10x^{-10-1}=-\frac{10}{x^{11}}$.