## How to Use the Product Rule

I would like to evaluate two more derivatives. They are $\frac{dx}{d\phi}\big|_{\phi^+}$ and $\frac{dz}{d\theta}\big|_{\theta^+}$ given $x = r \sin\theta\cos\phi$ and $z = r\cos\theta$.   Start with $\frac{dx}{d\phi}\big|_{\phi^+}$. The first…