# Partial Derivative – Calculating second order partial derivatives to a sum of simple functions in three variables – Exercise 4333

Exercise

Find second order partial derivatives of the function

$$u(x,y,z)=2x^3y+x^2z^3$$

$$u''_{xx} (x,y,z)=12yx+2z^3$$

$$u''_{yy} (x,y,z)=0$$

$$u''_{zz} (x,y,z)=6x^2z$$

$$u''_{xy} (x,y,z)=u''_{yx} (x,y,z)=6x^2$$

$$u''_{yz} (x,y,z)=u''_{zy} (x,y,z)=0$$

$$u''_{xz} (x,y,z)=u''_{zx} (x,y,z)=6xz^2$$

Solution

Coming soon…

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