What is the derivative of f(x)=ln(tan(x))f(x)=ln(tan(x)) ?

1 Answer
Aug 12, 2014

f'(x)=2(cosec2x)

Solution

f(x)=ln(tan(x))

let's begin with general example, suppose we have

y=f(g(x))

then, Using Chain Rule,

y'=f'(g(x))*g'(x)

Similarly following the given problem,

f'(x)=1/tanx*sec^2x

f'(x)=cosx/sinx*1/(cos^2x)

f'(x)=1/(sinxcosx)

for simplifying further, we multiply and divide by 2,

f'(x)=2/(2sinxcosx)

f'(x)=2/(sin2x)

f'(x)=2(cosec2x)