# derivative

## 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, $\frac{dy(\theta)}{d\theta} \bigg|_{\theta^+} = \sin\theta \frac{d r \sin \phi }{d\theta}\big|_{\theta^+} + r \sin \phi \frac{d \sin\theta }{d\theta}\big|_{\theta^+}$ Since $r \sin \phi$ does not depend on …

## 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 $\phi$, $r \cos\theta$ is a constant function with respect to $\phi$. From this post, it follows that \$ \boxed { \frac{dz}{d\phi} …