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Let f: [tex] \Re^3 \rightarrow \Re [/tex] be differentiable. Making the substitution

[tex] x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} [/tex]

(spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy, and df/dz.

I'm just not sure I understand the question. Does it involve pulling out a very long chain rule?

[tex] x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} [/tex]

(spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy, and df/dz.

I'm just not sure I understand the question. Does it involve pulling out a very long chain rule?

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