Question

What is the derivative of `sin (x/2)`?

Answer 1

`1/2 cos (x/2)`

Explanation:

if you know that `d/dx sin x = cos x` then you can use the chain rule so by letting `u = x / 2` you have `d/(du) sin u = cos u`

and `(du)/dx = (d)/dx (x/2)= 1/2`

`so d/{du} (sin u) \times (du)/(dx) = cos u \times 1/2 = 1/2 cos (x/2)`