Partial Differentiation of Composite Function |u = f(x/y, y/z, z/x), u = f(x−y, y−z, z−x)

📘 Calculus & Multivariable Calculus | Partial Differentiation Problem Solutions 📝 *Problem 1:* If u = f(x/y, y/z, z/x), prove that x(∂u/∂x) + y(∂u/∂y) + z(∂u/∂z) = 0. 🕘 *Problem 2 (at 9:00):* If u = f(x − y, y − z, z − x), prove that (∂u/∂x) + (∂u/∂y) + (∂u/∂z) = 0. 🎯 *Concepts Used:* ✔️ Partial Differentiation ✔️ Chain Rule for Multivariable Functions ✔️ Euler’s Theorem Type Relations ✔️ Simplification using Symmetry of Variables ✨ These problems beautifully illustrate how functions involving variable ratios or differences exhibit differential identities that simplify elegantly using multivariable calculus concepts. ✅ Very useful for Engineering Mathematics, Partial Differentiation, Multivariable Calculus, and VTU exam preparation. 💎 *Support Us:* Join this channel to support us & access exclusive perks 👇 🔗    / @officialmathematicstutor   #Calculus #PartialDifferentiation #MultivariableCalculus #VTUMaths #EngineeringMathematics #1BMATS101 #1BMATC101 #1BMATM101 #1BMATE101