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

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Answer 1 · 2018-03-21T15:09:39

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

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

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

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

= $1/cosx*(-sinx)$

= $-tanx$

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