The textbook indicates in section $7\mathrm{.}5$ that a differentiator could be constructed in a way analogous to the integrator circuit shown in Part One but using an inductor instead of a capacitor. While there are practical manufacturing reasons this isn't commonly done, there's no reason such a circuit can't be constructed, analyzed, and simulated.

A$.$ Consider the integrator circuit shown in Part One; determine what would need to change to use a resistor and an inductor instead to obtain a differentiator circuit. Choose convenient values for the resistance and inductance. Use nodal analysis and op amp rules to show that your design produces an output that is the derivative of an input sinusoidal voltage.

B$.$ Graph in MATLAB an input sinusoidal voltage $(8$ V at $2$ kHz $)$ and your predicted output.