I'm trying to find the fact that the Jacobi determinant (functional determinant) of the cartesian->spherical coordinate change is $r^2 \sin\theta$ in a mathematical reference book, "Taschenbuch der Mathematik" by Bronstein, Semendjajew, Musiol and Mühlig.
I've searched the index for "curvilinear", "Jacobi determinant" and "functional determinant", but can only find the general formula (determinant of the matrix of all first-order partial derivatives). Shouldn't this information be somewhere in a 1000-page work? Where should I look?