Question

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

Answer 1

`(dg)/(dx)=1/6sin(x/3)`

Explanation:

To differentiate `g(x)=sin^2(x/6)`, we use the concept of function of function, as `g(x)=(f(x))^2` where `f(x)=sin(x/6)`.

Hence, `(dg)/(dx)=(dg)/(df)*(df)/(dx)`

= `2sin(x/6)*cos(x/6)*1/6`

= `1/6sin(x/3)` (using formula `sin2x=2sinxcosx`)