How do you differentiate #log(sin^2(x))#?

1 Answer
Feb 10, 2017

#2cot(x)#

Explanation:

This answer assumes that #log(x)=log_e(x)#, the natural logarithm.

First use the rule #log(a^b)=blog(a)#:

#y=log(sin^2(x))=2log(sin(x))#

From here, we need to know that #d/dxlog(x)=1/x#. Through the chain rule, #d/dxlog(f(x))=1/f(x)*f'(x)#.

Then:

#dy/dx=2(1/sin(x))(d/dxsin(x))=2/sin(x)(cos(x))=2cot(x)#