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

Question

3330 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-13T15:41:55

Use the chain rule.

$f'(x) = 1/tanx d/dx(tanx)$

$= 1/tanx (-sec^2x)$

Now use trigonometry:

$= -cotxsec^2x$

$= -cosx/sinx 1/cos^2x$

$= -1/sinx 1/cosx$

$= -cscx secx$

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