Quotient rule/R/Power in denominator/Exercise

Let

$g,h\colon \mathbb {R} \longrightarrow \mathbb {R} _{+}$

denote differentiable functions, and set

${}f(x):={\frac {g(x)}{h(x)^{n}}}\,,$

${}n\in \mathbb {N} _{+}$. Show that the derivative of ${}f$ can be written as a fraction, with ${}h^{n+1}(x)$ as denominator.

Create a solution