# How do you differentiate y=ln(sin^(2) x)?

Apr 9, 2018

$y ' = 2 \cot x$

#### Explanation:

$\frac{d}{\mathrm{dx}} \ln u = \frac{1}{u} \mathrm{du}$

by applying this to the function:

$y ' = \frac{1}{\sin} ^ 2 x \left(\frac{d}{\mathrm{dx}} {\sin}^{2} x\right)$

$\frac{d}{\mathrm{dx}} {\sin}^{2} x = 2 \sin x \cos x$ power rule

so,
$y ' = \frac{1}{\sin} ^ 2 x 2 \sin x \cos x$

by simplification

$y ' = 2 \cos \frac{x}{\sin} x$=$2 \cot x$

You could also simplify the function to look like this:
$y = 2 \ln \sin x$
and it will be way easier that way.