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

1 Answer
Nov 11, 2015

f'(x) = -sin(ln(sinx))(1/sinx cosx) = cotxsin(ln(cscx))

Explanation:

Use the chain rule:

f'(x) = -sin(ln(sinx))[d/dx(ln(sinx))]

= -sin(ln(sinx))[1/sinx d/dx(sinx)]

= -sin(ln(sinx))[1/sinx cosx]

= sin(-ln(sinx)) cotx

= cotxsin(ln(1/sinx))

= cotxsin(ln(cscx))