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Partial Derivative – Calculating second order partial derivatives to x^m multiplied by y^n – Exercise 4317

Exercise 

Find second order partial derivatives of the function

z(x,y)=x^my^n

m,n parameters.

Final Answer

z''_{xx} (x,y)=m(m-1)x^{m-2}y^n

z''_{yy} (x,y)=n(n-1)y^{n-2}x^m

z''_{xy} (x,y)=z''_{yx}(x,y)=mnx^{m-1}y^{n-1}

Solution

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