# What is the derivative of #sin^-1(x)#?

##### 1 Answer

Apr 15, 2016

#### Explanation:

Let

so

Now differentiate implicitly:

#cosy dy/dx = 1# , so

#dy/dx = 1/cosy# .

Because

So we get:

#dy/dx = 1/sqrt(1-sin^2y) = 1/sqrt(1-x^2)# . (Recall from above#siny=x# .)