Question-60717

Question Number 60717 by peter frank last updated on 24/May/19

Commented by Prithwish sen last updated on 25/May/19

= | \begin{matrix} \frac{\partial x}{\partial r} \frac{\partial x}{\partial θ} \frac{\partial x}{\partial \emptyset} \\ \frac{\partial y}{\partial r} \frac{\partial y}{\partial θ} \frac{\partial y}{\partial ϕ} \end{matrix} |

| \begin{matrix} \frac{\partial z}{\partial r} \frac{\partial z}{\partial θ} \frac{\partial z}{\partial ϕ} \end{matrix} |

= \sin θ \cos ϕ (r^{2} \sin^{2} θ \cos ϕ) + \sin θ \sin ϕ (r^{2} \sin^{2} θ \sin ϕ)

+ \cos θ (r^{2} \sin θ \cos θ \cos^{2} ϕ + r^{2} c o s θ \sin θ \sin^{2} θ)

= r^{2} \sin^{3} θ (\cos^{2} ϕ + \sin^{2} ϕ) + r^{2} \sin θ \cos^{2} θ

= r^{2} \sin θ