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Solution assignment 07 Partial differentiation

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Assignment 7

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

f(x,y)=5xy+\displaystyle\frac{y}{x}

Solution

Some derivatives require differentiation of a fraction.

f_x=5y-\displaystyle\frac{y}{x^2}

f_y=5x+\displaystyle\frac{1}{x}

f_{xx}=\displaystyle\frac{2y}{x^3}

f_{yy}=0

f_{xy}=f_{yx}=5-\displaystyle\frac{1}{x^2}

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