y=log(sin^5(x))

y = log(sin

^{5}(x))Log identity: Log(a

^{b}) = b*log(a). Hence:y = log(sin

^{5}(x)) = 5log(sin(x))Now use the chain rule, letting u = sin(x)

y' = dy/dx = 5*dlog(u)/du* du/dx

y' = 5*(1/u)*(d(sin(x)/dx)

**y' = 5*cos(x)/sin(x) = 5cot(x)**