Question

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

Answer 1

`1/2cos(x/2)`

Explanation:

We use the chain rule, as we have `y(u(x))`

`(dy)/(dx) = (dy)/(du)(du)/(dx)`

`u = x/2 implies (du)/(dx) = 1/2`

`y = sin(u) implies (dy)/(du) = cos(u)`

`therefore (dy)/(dx) = cos(u)*1/2 = 1/2cos(x/2)`