use implcit differentiation to find dy/dx where y=(sin(7x))^x

Question

use implcit differentiation to find dy/dx where

y=(sin(7x))^x

Answer 1

y = [sin(7x)]^x

lny = xln[sin(7x)]

y' / y = ln[sin(7x)] + 7xcos(7x) / sin(7x)

y' / y = ln[sin(7x)] + 7xcot(7x)

y' = [sin(7x)]^x [ ln(sin(7x)) + 7xcot(7x)]