# What is the derivative of this function #y=sin^-1(x/3)#?

##### 1 Answer

Apr 6, 2017

#### Explanation:

I am going to assume that the

Looking at the differentiation of trigonometric functions, the derivative of

Proof:

If#y=arcsin(x)# , then#x=sin(y)# . Differentiating both sides with respect to#x# , we get#1=cos(y)dy/dx# . Then,#dy/dx=1/cos(y)# , which is equal to#1/sqrt(1-sin^2(y))# . But we said that#y=arcsin(x)# , so#dy/dx=1/sqrt(1-x^2)# .

In order to differentiate

Then,