Chapter 10, Problem 10.8E

The following operators and functions are defined:

$\begin{array}{cccc}\hat{\text{A}}=\frac{\partial }{\partial x}\left(\right)& \hat{B}=\sin \left(\right)& \hat{C}=\frac{1}{\left(\right)}& \hat{D}={10}^{\left(\right)}\\ p=4x^3-2x^{-2}& q=-0.5& r=45x{y}^2& s=\frac{2\pi x}{3}\end{array}$

Evaluate: (a) $\hat{\text{A}}p$ (b) $\hat{C}q$ (c) $\hat{B}s$ (d) $\hat{D}q$ (e) $\hat{\text{A}}\left(\hat{C}r\right)$ (f) $\hat{\text{A}}\left(\hat{D}q\right)$