Chapter 14.6, Problem 18E

To determine

(a)

To prove $g^{\prime }\left(x\right)=0$, thus $g\left(x\right)$ is constant function, where $g\left(x\right)=f\left(x,y\left(x\right)\right)$, where $f\left(x,y\right)=4-x^2{y}^2+e^{2x}$ and $y\left(x\right)=\frac{e^x}{x}$

To determine

(b)

To express $g\left(x\right)=f\left(x,y\left(x\right)\right)$ in terms of x and to show $g\left(x\right)$ is indeed a constant function