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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

Final Answer

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

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