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Solution assignment 04 Partial differentiation

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Assignment 4

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

f(x,y)=3xy-x\ln(y)

Solution

The logarithm seems a problem, but this is not the case.

f_x=3y-\ln(y)

f_y=3x-\displaystyle\frac{x}{y}

f_{xx}=0

f_{yy}=\displaystyle\frac{x}{y^2}

f_{xy}=f_{yx}=3-\displaystyle\frac{1}{y}

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