Partial Differentiation | Multivariable Calculus | u=e^(ax + by) f(ax − by), b(∂u/∂x)+a(∂u/∂y)=2abu
Автор: Mathematics Tutor
Загружено: 2025-01-28
Просмотров: 3365
📘 Calculus & Multivariable Calculus | Partial Differentiation Problem Solution
📝 Problem Statement:
If
u = e^(ax + by) · f(ax − by),
then 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.
#Calculus #PartialDifferentiation #MultivariableCalculus #EngineeringMathematics #VTU #ChainRule #ExponentialFunctions #BMATS201 #BMATE201 #BMATC201 #BMATM201 #1BMATS101 #1BMATE101 #1BMATC101 #1BMATM101 #Module1 #Module2
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