Chain Rule in Partial Differentiation | 4 Most Important Proof Problems | Engineering Mathematics

In this video, we solve four important proof-based problems from Partial Differentiation using Chain Rule and transformation techniques. ✔ Question 9: Prove that ∂x 2 ∂ 2 u ​ + ∂y 2 ∂ 2 u ​ + ∂z 2 ∂ 2 u ​ =m(m+1)r m−2 ✔ Question 10: Prove that x 1 ​ ∂x ∂u ​ + y 1 ​ ∂y ∂u ​ + z 1 ​ ∂z ∂u ​ =0 ✔ Question 11: Chain Rule Transformation Problem x ∂x ∂z ​ −y ∂y ∂z ​ = ∂u ∂z ​ − ∂v ∂z ​ ✔ Question 12: Important Change of Variables Problem x ∂y ∂z ​ −y ∂x ∂z ​ =(1+v 2 ) ∂v ∂z ​ #EngineeringMathematics #PartialDifferentiation #ChainRule #MultivariableCalculus #PDE #EngineeringMaths #BTechMaths #UniversityExam #SolvedExamples