Hey, im a college student at the university of oklahoma and couldnt figure out this problem, help would be greatly appreciated!

(A)

Find the linearization of the spherical change of coordinates map:

$\displaystyle

f(p; \phi; \theta) = (p)\cos(\theta)\sin(\phi) ; (p)\sin(\theta)\sin(\phi) ; (p)\cos(\phi)

$

(B)

Find the factor by which the linear map you found in (A) scales volume.