# How do you find the derivative of #arcsin (x/2)#?

##### 1 Answer

Dec 1, 2016

#### Explanation:

Let

#sin(y)=x/2#

Differentiate both sides with respect to

The right hand side's derivative is

#cos(y)*dy/dx=1/2#

We can write

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

Since

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

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

Taking the

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

Multiplying both sides by

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

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

Thus the derivative of