Derivative No. 7

Using the methods in this post, I would like to evaluate $\frac{dy(\theta)}{d\theta}\bigg|_{\theta^+}$ with $y(\theta)=r\sin\theta\sin\phi$ Substituting, the expression to evaluate is $ \frac{d \sin \theta r \sin \phi  }{d\theta} \bigg|_{\theta^+}$. From the product rule, $…

Read more

Derivative No. 6

Using the methods in this post, I would like to evaluate $\frac{dx(\theta)}{d\theta}\bigg|_{\theta^+}$ with $x(\theta)=r\sin\theta\cos\phi$. Substituting, the expression to evaluate is $ \frac{d r \sin\theta \cos \phi }{d\theta} \bigg|_{\theta^+}$. From the product rule, $ \frac{dx(\theta)}{d\theta}…

Read more

Derivative No. 5

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