Find the first, second, and cross partial derivatives for the following function:f(x,y) = 12x4 – 6x²y + 4xy³

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Find the first, second, and cross partial derivatives for the f(x, y) = 12x4 – 6x²y + 4xy3 %3D

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 36E

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Question

Find the first, second, and cross partial derivatives for the following function:
f(x,y) = 12x4 – 6x²y + 4xy³

Expert Solution

Step 1

Introduction:

When a function is multivariable, we follow the partial derivative to find the differentiation. In the case of a multivariable function, the function changes when one of the independent variables changes. Thus, in the case of partial derivative, when we determine the rate of change of the function with respect to a particular variable, all other variables are treated as constant. A function is given in the question. We determine the first, second, and cross derivatives of the function.