find-w-and-w-given-that-w-x-y-z-f-x-2-y-2-z-2-where-x-rcos-cos-y-rcos-sin-z-rsin-

Tinku Tara June 4, 2023 Differentiation 0 Comments

Question Number 126478 by BHOOPENDRA last updated on 20/Dec/20

find (∂w/∂θ) and (∂w/∂φ) given that w(x,y,z)=f(x^2 +y^2 +z^2 ) where x=rcosθcosφ y=rcosθsinφ,z=rsinθ.

$${find}\:\frac{\partial{w}}{\partial\theta}\:{and}\:\frac{\partial{w}}{\partial\phi}\:{given}\:{that}\: \\ $$$${w}\left({x},{y},{z}\right)={f}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)\:{where}\:{x}={rcos}\theta{cos}\phi \\ $$$${y}={rcos}\theta{sin}\phi,{z}={rsin}\theta. \\ $$

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find-w-and-w-given-that-w-x-y-z-f-x-2-y-2-z-2-where-x-rcos-cos-y-rcos-sin-z-rsin-

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