Partial Differentiation | Total Derivative du/dt | u=xy+yz+zx, x=tcos t, y=tsin t, z = t at t = π/4

📘 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 💎 *Support Us:* Join this channel to support us & access exclusive perks 👇 🔗 https://www.youtube.