If `y=log_(cosx)sinx,` then `(dy)/(dx)` is equal to

Options

A. `(cot x log cos x+tan x log sin x)/((log cos x)^(2))`
B. `(tan x log cos x+cot x log sin x)/((log cosx)^(2))`
C. `((cot x log x+tan x log sinx))/((log sin x)^(2))`
D. None of these

Answer

A

Explanation

Given `y=log_(cos x) sin x=(log sinx)/(log cos x)`
On differentiating w.r.t.x., we get
`(dy)/(dx)=(cot x.log cos x +tan x. log sin x)/((log cos x)^(2))`