# How do you differentiate #y = arcsin(x/2)#?

##### 1 Answer

Jun 18, 2015

Apply the chain rule to the derivative of

#### Explanation:

You may want a more full treatment of Differentiating Inverse Sine

Applying the chain rule, we get:

In this question

We get

We're done with calculus, but this can be 'cleaned up' algebraically:

#= 1/(2 sqrt (1-x^2/4)#

#= 1/(2 sqrt ((4-x^2)/4)#

#= 1/(2 sqrt (4-x^2)/sqrt4)#

#= 1/(cancel(2) sqrt (4-x^2)/cancel(sqrt4))#

# = 1/sqrt(4-x^2)#