# How do you differentiate #sin^2(x/6)#?

##### 1 Answer

Aug 19, 2015

#### Explanation:

You can differentiate this function

#y = sin(x/6)#

by using the chain rule twice, once for

Your target derivative will be

#d/dx(y) = d/(du_1)(u_1^2) * d/dx(u_1)# , with

#d/dxu_1 = d/(du_2) * sinu_2 * d/dx(u_2)#

This will give you

#d/dx(u_1) = cosu_2 * d/dx(x/6)#

#d/dx(sin(x/6)) = cos(x/6) * 1/6#

Plug this back into your target derivative to get

#y^' = 2u_1 * 1/6 * cos(x/6)#

#y^' = color(green)(1/3 * sin(x/6) * cos(x/6))#