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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Find the first, second, and cross partial derivatives for the following function:
f(x,y) = 12x4 – 6x²y + 4xy³
Transcribed Image Text: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. 

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