Question

determine all second order partial derivatives for f(x,y)=In 3xy3

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The answers are $\bf\frac{-1}{x^2}$, $\bf\frac{-3}{y^2}$ and 0.

Given:

$f(x,y)=\ln 3xy^3$

To Find:

All second-order partial derivatives

Solution:

The second-order partial derivatives are $\frac{d^2}{dy^2}$, $\frac{d^2}{dx^2}$ and $\frac{d^2}{dydx}$.

Hence the second-order partial derivatives are

$\frac{d^2\ln 3xy^3}{dx^2} = \frac{-1}{x^2}\\ \\\frac{d^2\ln 3xy^3}{dy^2} = \frac{-3}{y^2}\\\\\frac{d^2\ln 3xy^3}{dxdy} =0$

The second-order partial derivatives are $\bf\frac{-1}{x^2}$, $\bf\frac{-3}{y^2}$ and 0.

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