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

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Answer 1 · 2015-12-09T19:10:31

$\frac{{sec}^{2} x}{tan x}$ $(sec^2x)/tanx$

Using the following standard differentiation rules in conjunction :

$\frac{d}{d x} ln u (x) = \frac{1}{u} \cdot \frac{d u}{d x}$ $d/dx lnu(x)=1/u*(du)/dx$

$\frac{d}{d x} tan x = {sec}^{2} x$ $d/dx tanx = sec^2x$

we get that

$\frac{d}{d x} ln (tan x) = \frac{1}{tan x} \cdot {sec}^{2} x$ $d/dx ln(tanx)=1/tanx*sec^2x$

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