# How do you differentiate #y=csc^-1(3x)#?

##### 1 Answer

Nov 25, 2016

Rewrite since

#csc(y)=3x#

Differentiate both sides. On the left-hand side, don't forget that the chain rule will apply.

#-csc(y)cot(y)dy/dx=3#

Note that on the left-hand side,

#-3xsqrt(9x^2-1)dy/dx=3#

#dy/dx=-1/(xsqrt(9x^2-1))#