Find derivative(use logrithmic functions).

Question

y=x^-cosx

Answer 1

y=x^-cosx
ln y = -cos x ln x

d/dx( ln y ) = d/dx (-cos x lnx)

(1/y)dy/dx = (-cos x) / x + ln x sin x

dy/dx = [ln x sin x - (1/x) cos x] /y

= [ln x sin x - (1/x) cos x] x^cos x

Answer 2

dy/dx = [ln x sin x - (1/x) cos x] y

= [ln x sin x - (1/x) cos x] x^cos-x