# Partial Derivative – Calculating second order partial derivatives to a sum of simple functions – Exercise 4310

Exercise

Find second order partial derivatives of the function

$$z(x,y)=x^3+3xy^2-4x^2y^5+1$$

$$z''_{xx} (x,y)=6x-8y^5$$
$$z''_{yy} (x,y)=6x-80x^2y^3$$
$$z''_{xy} (x,y)=z''_{yx}(x,y)=6y-40xy^4$$