Question

find f'(x) if f(x)= (cosx)^sinx

Answer 1

let y = cos x^sinx

take ln of both sides
ln y = sinx ln(cosx)
(dy/dx)/y = sinx(-sinx/cosx) + cosx(ln(cosx))

dy/dx = (cos x^sinx )(sinx(-sinx/cosx) + cosx(ln(cosx)) )

simplify as needed