What is the derivative of #f(x)=log(sin^2(x))#?

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Answer 1 · 2016-06-06T08:51:10

#f' (x)=2*log e*cot x#

From the given #f(x) = log (sin^2 x)#

The formula for finding the derivative of logarithm

#d/dx(log_a u)=1/u*log_a e*d/dx(u)#

#d/dx(f(x))=d/dx(log (sin^2 x))=1/sin^2 x*log e*d/dx(sin^2 x)#

#d/dx(f(x))=d/dx(log (sin^2 x))=1/sin^2 x*log e*2*sin x*cos x#

#d/dx(f(x))=2*log e*cot x#

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