Maths Question: I am having a lot of problems with this question, can any undergrad physicists or mathematicians help me?(adsbygoogle = window.adsbygoogle || []).push({});

(note: p before a differntial= partial derivative) .

Spherical polar coordinates (r, (thetha), (phi)) are defined in terms of Cartesian coorindates (x,y,z) by:

x=rsin(theta)cos(phi)

y=rsin(theta)sin(phi)

z=rcos(theta)

given that f is a function of r only, independent of theta and phi, show that

p(df)/p(dx) = (x/r).(df/dr)

p(d^2f)/p(dx^2) = (1/r).(df/dr) + (x^2/r).d[(1/r).(df/dr)]/dr

and hence deduce that:

p(d^2f)/p(dx^2) + p(d^2f)/p(dy^2) + p(d^2f)/p(dz^2) =

(1/r^2).d[r^2.(df/dr)]/dr

a) is straigthforward, any thoughts on how to appraoch b) ???

thanks

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# Partial differentiation and changing variables

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