Compute all the first and second partial derivatives of the function. We assume that y>0𝑦>0 .f(x,y)=xy−3x−ln(y6) .

Question

Compute all the first and second partial derivatives of the function. We assume that y>0𝑦>0 .f(x,y)=xy−3x−ln(y6) .
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Solution 1

First, let's compute the first partial derivatives:

  1. Partial derivative with respect to x (∂f/∂x):

    ∂f/∂x = y - 3

  2. Partial derivative with respect to y (∂f/∂y):

    ∂f/∂y = x - 6/y

Now, let's compute the second partial derivatives:

  1. Second partial derivative with respect to x (∂²f/∂x²): Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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