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Solution assignment 02 Partial differentiation

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Assignment 2

Calculate the first, second and mixed partial derivatives of the following function.

f(x,y)=x^3+4y^2+2xy-3

Solution

A minor difficulty is the term 2xy.

f_x=3x^2+0+2y-0=3x^2+2y

f_y=0+8y+2x-0=2x+8y

f_{xx}=6x+0=3

f_{yy}=0+8

f_{xy}=f_{yx}=2

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