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Homework Statement:

##x=r sin\theta cos\phi, y=rsin\theta sin\phi, z=rcos\theta##
Find ##\delta f/\delta x##and##\delta r/\delta x## treating r as a function of the cartesian coordinates
Given f is a function of r only, show
##\delta f^2/\delta x = (x/r)(df/dr)##
and
##\delta ^2 *f/\delta x^2 = (1/r)(df/dr) + (x^2/r)(d/dr)(1/r)(df/dr)##
Homework Equations:
 ?
Ive found ##\delta x/\delta r## as ##sin\theta cos\phi##
##\delta r/\delta x## as ##csc\theta sec\phi##
But unsure how to do the second part? Chain rule seems to give r/x not x/r?
##\delta r/\delta x## as ##csc\theta sec\phi##
But unsure how to do the second part? Chain rule seems to give r/x not x/r?
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