Question

How do you find the derivative of y=ln(cos(x))y=ln(cos(x)) ?

Answer 1

`y=ln(cosx)\\\\We\ know:\\(lnx)'=(1)/(x)\ and\ (cosx)'=-sinx\ and\ \{f[g(x)]\}'=f'[g(x)]\cdot g'(x)\\\\therefore:\\\\y'=(1)/(cosx)\cdot(-sinx)=-(sinx)/(cosx)=-tanx`