Derivatives Of Functions In Parametric Forms

Given : (x + y) sin U =

x%5E2y%5E2

%5Cleft(x%2By%5Cright)%5Csin%20U%20%3Dx%5E%7B2%7Dy%5E%7B2%7D

%5CRightarrow%20%5Csin%20U%20%3D%20%5Cfrac%7Bx%5E%7B2%7Dy%5E%7B2%7D%7D%7Bx%2By%7D%20%3Dv

(let)
Here n = 2 - 1 = 1
Euler's theorem

x.%20%5Cfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20x%7D%20%2By.%20%5Cfrac%7B%5Cpartial%20v%7D%7B%5Cpartial%20y%7D%20%3Dnv

%5Ctherefore%20x%20%5Cfrac%7B%5Cpartial%5Csin%20U%7D%7B%5Cpartial%20x%7D%20%2B%20y%20%5Cfrac%7B%5Cpartial%5Csin%20U%7D%7B%5Cpartial%20y%7D%20%3D%5Csin%20U

%5CRightarrow%20x.%5Ccos%20U%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20x%7D%20%2By%20.%5Ccos%20U.%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20y%7D%20%3D%5Csin%20U

%5CRightarrow%20x%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20x%7D%20%2By%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20y%7D%20%3D%20%5Cfrac%7B%5Csin%20U%7D%7B%5Ccos%20U%7D%20%3D%5Ctan%20U

%5CRightarrow%20x%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20x%7D%20%2B%20y%20%5Cfrac%7B%5Cpartial%20U%7D%7B%5Cpartial%20y%7D%20%3D%5Ctan%20U

Chapter Questions
1 MCQs