Partial Differentiation | Total Derivative du/dt | u=xy+yz+zx, x=tcos t, y=tsin t, z = t at t = π/4
Автор: Mathematics Tutor
Загружено: 2024-10-12
Просмотров: 15444
📘 Calculus & Multivariable Calculus | Total Derivative Problem Solution | Chain Rule
📝 Problem Statement:
Find *du/dt* for the function
**u = xy + yz + zx**,
where
x = t cos t, y = t sin t, z = t,
at **t = π/4**, using the chain rule.
🎯 Concepts Used:
✔️ Total Derivative of a multivariable function
✔️ Partial Differentiation (∂u/∂x, ∂u/∂y, ∂u/∂z)
✔️ Chain Rule: du/dt = (∂u/∂x)(dx/dt) + (∂u/∂y)(dy/dt) + (∂u/∂z)(dz/dt)
✔️ Substitution and evaluation at t = π/4
✨ This problem demonstrates how to compute the derivative of a multivariable function with respect to a single variable when each variable is a function of that variable. A common type of problem in *VTU exams* and Engineering Mathematics to strengthen chain rule applications.
✅ Very useful for Engineering Mathematics, Partial Differentiation, Multivariable Calculus, and VTU exam preparation.
#Calculus #PartialDifferentiation #MultivariableCalculus #ChainRule #TotalDerivative #VTU #EngineeringMathematics #BMATS201 #BMATE201 #BMATC201 #BMATM201 #1BMATS101 #1BMATE101 #1BMATC101 #1BMATM101 #Module1 #Module2
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