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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

Final Answer

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

Solution

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