Using the methods in this post, I would like to evaluate $\frac{dy(\phi)}{d\phi}\bigg|_{\phi^+}$ with $y(\phi)=r\sin\theta\sin\phi$. Substituting, the expression to evaluate is $\frac{d r \sin \theta \sin \phi }{d\phi} \bigg|_{\phi^+}$. From the product rule, $… Read more ## Derivative No. 4 Using the methods in this post, I would like to evaluate$\frac{dz}{d\phi}\bigg|_{\phi^+}$with$z=r\cos\theta$. Substituting, the expression to evaluate is$ \frac{d (r \cos\theta )}{d\phi} \bigg|_{\phi^+}$. Since$ r \cos\theta $does not depend on… Read more ## Derivative No. 3 Using the methods in this post, I would like to evaluate$\frac{dz(r)}{dr}\bigg|_{r^+}$with$z(r)=r\cos\theta$. Substituting, the expression to evaluate is$ \frac{d (r \cos\theta)}{dr} \bigg|_{r^+}$. From the product rule,$ \frac{dz(r)}{dr} \bigg|_{r^+} = r \frac{d(…

Using the methods in this post, I would like to evaluate $\frac{dy(r)}{dr}\bigg|_{r^+}$ with $y(r)=r \sin\theta\sin\phi$. This method is not the traditional method taught in a Calculus course because I only want to use…