Derivative of [w^(3 / 2)] * [w + ce^w]

Find the derivative of [w^(3 / 2)] * [w + ce^w].

I got [(5w^(3 / 2)) / 2] + [(2c(e^w)w^(3 / 2)) / 2] + [(3c(e^w)w^(1 / 2)) / 2].

Which, just to clarify, is the same thing as:
http://www.wolframalpha.com/input/?i=derivative+%5Bw%5E%283+%2F+2%29%5D+*+%5Bw+%2B+ce%5Ew%5D
correct?

Chain rule.

Derivative first times second + second times derivative of first.

(3/2)w^(1/2)(w + ce^w) + w^(3/2) * (1 + ce^w)

Assuming you're taking the derivative with respect to w.

And yes, your answer is correct.