Your solutions are correct.
This is what I got so far
a) f(x) = sqrt(x)(2x+3)^2
f'(x)= (1/2x^-1/2)(1)(2x+3)^2 + (x^1/2)(2)(2x+3)(2)
not sure how to simplify it more
b)h(x) = 3e^(sin(x+2))
= (3)(e^(sin(x+2))(cos(x+2))
I have a feeling that the exponent of e is suppose to be different, maybe I missed a step with the (x+2)