# What is the derivative of #y = ln(cscx)#?

##### 2 Answers

Aug 22, 2016

We will use the chain rule to differentiate. Let

The derivative of

The derivative of

Hopefully this helps!

Apr 5, 2018

Alternatively, using logarithm laws, we can say:

#y = ln(1/sinx) = ln(1) - ln(sinx) = 0 - ln(sinx) = -ln(sinx)#

It follows by the chain rule that

#y' = cosx * -1/sinx = -cosx/sinx = -cotx#

Hopefully this helps!