I didn't check whole the answer but I notice a mistake by calculating with the chain rule:
Which is different from your answer.
I have this problem which I am stuck on. It tells me to find the derivative of the function in 2 ways...first by substitution then by the chain rule using partial derivatives. I found the first one fine using substitution then taking a derivative. The second one I came up with a different answer (which I believe is incorrect). Can someone help me get unstuck please? I've attached a picture of my work. Thanks