partial derivative $ e^{\frac{x^2}{2}}y $

Question

$ e^{\frac{x^2}{2}}y $ find $ f_{xxxxxxxxxxxxxxxxxxxxxxxyxxxxxxxxxxxxyxxxxxxx} $

I already worked out 6 terms but still cannot see any pattern. am i suppose to do all these?

Answer 1

What is the value of

$$\frac{\partial^2}{\partial y^2}e^{\frac{x^2}{2}}y$$

Answer 2

As they are partial derivatives the order you do them is not important. So start with the easier ones and see what you get.