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)