find y' if y=(sinx)^2 + 2^(sinx)

find y' if $\displaystyle y=(sinx)^2 + 2^{sinx}$

I don't really know which definitions/properties to use in this instance, but what I've tried is:

Dx$\displaystyle a^{x} = a^{x}\ln{a}$

First, I separated the two terms and took the derivative of both

Dx$\displaystyle (sinx)^2 = (sinx)^2\ln{sinx}$

Dx $\displaystyle 2^{sinx} = 2(sinx)(cosx)$ (Chain Rule)

Giving:$\displaystyle (sinx)^2\ln{sinx} + 2(sinx)(cosx)$

Any chance that I did this right? If not, am I using the wrong properties for the first term? Thanks!!