If (x²/a²+u)+(y²/b²+u)+(z²/c²+u)=1, prove that (∂u/∂x)²+(∂u/∂y)²+(∂u/∂z)²=2(x ∂u/∂x+y∂u/∂y+z∂u/∂z)​

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If x^2 /a^2 +u + y^2/ b^2 +u + z^2/ c^2 + u = 1 prove that If x^2 /a^2 +u + y^2/ b^2 +u + z^2/ c^2 + u = 1 prove that
Partial Differentiation | Multivariable Calculus | u = 1/√(x² + y² + z²), ∂²u/∂x²+∂²u/∂y²+∂²u/∂z²= 0 Partial Differentiation | Multivariable Calculus | u = 1/√(x² + y² + z²), ∂²u/∂x²+∂²u/∂y²+∂²u/∂z²= 0
If x^/a^2+u+y^2/b^2+u+z^2/c^2+u=1,prove that (du/dx)^2+(du/dy)^2+(du/dz)^2=2(du/d+du/d+du/dz) If x^/a^2+u+y^2/b^2+u+z^2/c^2+u=1,prove that (du/dx)^2+(du/dy)^2+(du/dz)^2=2(du/d+du/d+du/dz)
Partial derivatives - Laplace equation Partial derivatives - Laplace equation
If u = f(x² + 2yz , y² + 2zx), prove that (y² - zx)(∂u/∂x) + (x² - yz)(∂u/∂y) + (z² - xy)(∂u/∂z) = 0 If u = f(x² + 2yz , y² + 2zx), prove that (y² - zx)(∂u/∂x) + (x² - yz)(∂u/∂y) + (z² - xy)(∂u/∂z) = 0
IF U=1/√X²+Y²+Z² WHERE X²+Y²+Z²=0 THEN PROVE THAT ∂²U/∂X²+ ∂²U/∂Y²+ ∂²U/∂Z²=0. IF U=1/√X²+Y²+Z² WHERE X²+Y²+Z²=0 THEN PROVE THAT ∂²U/∂X²+ ∂²U/∂Y²+ ∂²U/∂Z²=0.
From PDE x²/a²+y²/b²+z²/c² full solution From PDE x²/a²+y²/b²+z²/c² full solution
Do You Remember How Partial Derivatives Work? 🤔 #Shorts #calculus #math #maths #mathematics Do You Remember How Partial Derivatives Work? 🤔 #Shorts #calculus #math #maths #mathematics