Sections $5\mathrm{.}3,5\mathrm{.}4,$ and $5\mathrm{.}8$

$(5$ pts$)$ Evaluate each of the following. Explain how they are alike and different. Show all steps and state which theorem$/$definition is used at each step.

a$.\frac{d}{dx}{\displaystyle \underset{0}{\overset{x}{}}}{e}^{arctant}dt$

b$.\frac{d}{dx}{\displaystyle \underset{0}{\overset{1}{}}}{e}^{arctant}dt$