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Differentiable functions

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Let f: ℝ3 → ℝ be differentiable. Making the substitution
x = ρ cos(θ) sin(φ), y = ρ sin(θ) sin(φ), z = ρ cos(φ)
(spherical coordinates) into f:(x,y,z), compute

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Solution Summary

This provides an example of working with differentiable functions and substitutions.