Find the first-order and second-order partial derivatives of the following functions: (x,y) =x2y3

Find the first-order and second-order partial derivatives of the following functions:

(x,y) =x²y³

Solutions

Expert Solution

Z = f(x, y) = x²y³

(1) First-order partial derivatives are:

Zx = Z/x = 2xy³

Zy = Z/y = 3x²y²

(2) Second-order partial derivatives are:

Zxx = /x(Z/x) = 2y³

Zyy = /y(Z/y) = 6x²y

Zxy = /y(Z/x) = 6xy²

Zyx = /x(Z/y) = 6xy²

Rahul Sunny answered 1 year ago

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