Question

Find the derivative of the following functions (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) : $\cos ecx\cot x$

Answer 1

let $f\left(x\right)=\cos ecx\cot x$
By Leibnitz product rule
$f^{\prime }\left(x\right)=\cos ec\times {\left(\cot x\right)}^{\prime }+\cot x{\left(\cos ecx\right)}^{\prime }$
$=\cos exx(-\cos e{c}^{2}x)+\cot x(-\cos ecx\cot x)$
$=-\cos e{c}^{3}x-{\cot }^{2}x\cos ecx$