if F(x) = sin^5 (x/6) + cos^4 (x/3)

find F'(x)

I'm doing the wrong derivative, i thought that the derivative of

sin(x/6) = cos (x/6)

but that doesn't seem to be correct.

Let's say we're looking at

(sin(x/6))^5 ( i took the 5 out for chain rule purposes)

then

5(sin(x/6))^4 is the derivative of the outside applied to the inside,

and the derivative of the inside(sin(x/6)) is x/6 * (cos(x/6))??

i thought that the derivative would be

5(sin(x/6))^4 * (cos(x/6))

is there a rule for the x/6 to come out of there?

I can solve the problem, i just need to figure out if i'm missing something specifically with the derivative.

i can't exactly keep going if the derivative is wrong

thanks a bunch