# Partial Derivative – Calculating second order partial derivatives to e to the power of a function – Exercise 4327

Exercise

Find second order partial derivatives of the function

$$z(x,y)=e^{x^2y}$$

$$z''_{xx} (x,y)=2ye^{x^2y}(2x^2y+1)$$
$$z''_{yy} (x,y)=x^4e^{x^2y}$$
$$z''_{xy} (x,y)=z''_{yx}(x,y)=2xe^{x^2y}(x^2y+1)$$