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can someone help me find the derivative for this function?

y=log(sin^5(x))

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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y = log(sin5(x))
 
Log identity:  Log(ab) = b*log(a).  Hence:
 
y = log(sin5(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)