Question

Find the derivative of the following fuctions (it is to be understood that $a,b,c,d,p,q,r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{x}{{\sin }^{2}x}$

Answer 1

Let $f\left(x\right)=\frac{x}{{\sin }^{2}x}$
Thus by quotient rule
$f^{\prime }\left(x\right)=\frac{{\sin }^{2}x\frac{d}{dx}x-x\frac{d}{dx}{\sin }^{2}x}{{\sin }^{4}x}=\frac{{\sin }^{2}x-x\sin 2x}{{\sin }^{4}x}$