Question

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

Answer 1

`(df)/(dx)=-tanx`

Explanation:

We have `f(x)=ln(cosx)`, let `g(x)=cosx`, then `f(x)=ln(g(x))`

Now using chain formula `(df)/(dx)=(df)/(dg(x))*(dg(x))/dx`

= `1/(g(x))*(-sinx)`

= `1/cosx*(-sinx)`

= `-tanx`