Question

What is the derivative of?

Answer 1

Answer:

cot(x)

Explanation:

$\frac{d}{dx}ln(sin(x))$

Use u-substitution,

$u=sin(x)\\u'=cos(x)$

$\frac{d}{dx}ln(sin(x)) = \frac{d}{du}ln(u)$

$= \frac{1}{u}u'$     //using the chain rule

$= \frac{1}{sin(x)}cos(x)$

$=cot(x)$