question_answer

If \[y={{(\sin x)}^{\tan x}},\] then \[\frac{dy}{dx}\] is equal to

A)  \[{{(\sin \,\,x)}^{\tan x}}(1+{{\sec }^{2}}x\,\,\log \,\,\sin \,\,x)\]

B)  \[\tan \,\,x\,\,{{(\sin \,\,x)}^{\tan x-1}}\cos \,\,x\]

C)  \[{{(\sin x)}^{\tan x}}{{\sec }^{2}}x\,\,\log \,\,\sin \,\,x\]

D)  \[\tan \,x\,{{(\sin \,x)}^{\tan x-1}}\]

E)  None of these