`g(alpha) = 5^(-alpha/2)sin(2alpha)` Find the derivative of the function

We shall use:

Product rule

`(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)`

Chain rule

`(f(g(x)))'=f'(g(x))g'(x)`

First we apply product rule.

`g'(alpha)=(5^(-alpha/2))'sin(2alpha)+5^(-alpha/2)(sin(2alpha))'=`

Now we apply chain rule to the composite functions we need to derivate.

 `5^(-alpha/2)ln (5)cdot(-1/2) sin(2alpha)+5^(-alpha/2)cos(2alpha)cdot2`