how do you differentiate tan(x)^cos(x)

Question

 I have no idea how to solve this

Answer 1

y=tan(x)^cos(x)  (take log from both sides)

lny=cos(x)ln(tanx) (take derivative form both sides)

y'/y=(cos(x)ln(tan(x)))'=-sin(x)ln(tan(x))+1/sin(x)

y'=y sin(x)(1/sin²(x)-ln(tan(x))