Mathematical Exercise: Exploring the Function w=f(x,y,z)

A photo of handwritten math notes showing a complex calculus problem involving spherical coordinates and the chain rule. The text includes an exercise to prove a Laplacian identity, followed by a hand-drawn 'auxiliary diagram I' with nodes labeled w, x, y, z, ρ, φ, θ and connecting lines. Below the diagram, text states 'By auxiliary diagram I and the chain rule we have' followed by three equations applying the chain rule. The joke is that the diagram is absurdly complex and unnecessary for the proof, mocking over-engineered academic solutions.

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