If u=f(r), where r^2 = x^2 + y^2 , show that d^2 z/dx^2 +d^2 z/dy^2 = f"(r)+1/r f'(r)

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If u=f(r) where r^2=x^2+y^2, show that ∂^2u/∂x^2+∂^2u/∂y^2=f''(r)+1/r f'(r)| Partial Differentiation

if u=f(r) where r^2=x^2+y^2, show that d^2u/dx^2 +d^2u/dy^2 = f"(r)+1/r f'(r).

If u=f(r) where r2=x2+y2+z2 then dx2d2u​+dy2d2u​+dz2d2u​=f"(r)+r4​f′(r) partial differentiation

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If u = 𝐫^𝐦, where 𝐫^𝟐 = 𝐱^𝟐+𝐲^𝟐+𝐳^𝟐,then prove that (𝐝^𝟐 𝐮)/(𝐝𝐱^𝟐 ) + (𝐝^𝟐 𝐮)/(𝐝𝐲^𝟐 ) + (𝐝^

302/1000 | Proof: Partial Differentiation of u = f(r) where r² = x² + y² | Second Order Derivatives

Partial Derivatives - Multivariable Calculus

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