Find derivative using logarithmic differentiation

Question

F(x)= secx^cotx

Answer 1

f = secx^cotx
log f = cotx * log secx
1/f f' = (-csc^2 x * log secx) + (cotx * secx*tanx/secx)
f' = secx^cotx (1 - csc^2(x) log secx)