Find the Jacobian of the transformation x=rcosθsinϕ,y=rsinθsinϕ,z=rcosϕx = r \cos \theta \sin \phi, y = r \sin \theta \sin \phi, z = r \cos \phix=rcosθsinϕ,y=rsinθsinϕ,z=rcosϕ.
rrr
r2sinϕr^2 \sin \phir2sinϕ
rsinϕr \sin \phirsinϕ
r2cosϕr^2 \cos \phir2cosϕ