# What is the derivative of #y=arcsin(3x )#?

##### 1 Answer

Oct 16, 2016

#### Explanation:

An alternative method that doesn't require knowing the derivative of

#y=arcsin(3x)#

#sin(y)=3x#

Differentiate both sides with respect to

#cos(y)dy/dx=3#

Solving for the derivative,

#dy/dx=3/cos(y)#

We know that

#dy/dx=3/sqrt(1-sin^2(y))#

Since

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

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