Partial Differentiation | Multivariable Calculus | u=e^(ax+by) · f(ax–by), b(∂u/∂x)+a(∂u/∂y) = 2abu

Автор: Mathematics Tutor

Загружено: 2023-11-29

Просмотров: 10083

Описание:

📘 Calculus & Multivariable Calculus | Partial Differentiation Problem Solution

📝 Problem Statement:
If
u = e^(ax + by) · f(ax – by),
prove that
b(∂u/∂x) + a(∂u/∂y) = 2ab u.

🎯 Concepts Used:
✔️ Partial Differentiation
✔️ Chain Rule for Functions of Multiple Variables
✔️ Derivatives of Exponential Functions
✔️ Simplification using Algebraic Manipulation

✨ This problem demonstrates how to apply the chain rule and partial derivatives to functions of combined variables to verify a given relation, a common type of problem in Engineering Mathematics and VTU exams.

✅ Very useful for Engineering Mathematics, Partial Differentiation, Multivariable Calculus, and VTU exam preparation.

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Partial Differentiation | Multivariable Calculus | u=e^(ax+by) · f(ax–by), b(∂u/∂x)+a(∂u/∂y) = 2abu

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