Differentiate the following w.r.t x: $\sin^mx.\cos ^nx$.

Question

$\begin{array}{1 1} (A)\;\sin^mx.\cos^nx(-n\tan x+m\cot x) \\ (B)\;-\sin^mx.\cos^nx(-n\tan x+m\cot x) \\(C)\;\sin^mx.\cos^nx(n\tan x+m\cot x) \\ (D)\;\sin^mx.\cos^nx(-n\tan x-m\cot x)\end{array}$