Exercise 1

The functions $\fe{f}{x}=e^{3x}$, $\fe{g}{x}=\left(e^x\right)^3$, and $\fe{h}{x}=\left(e^3\right)^x$ are equivalent. Find the first derivative formulas for each of the functions (without altering their given forms) and then explicitly establish that the derivative formulas are the same.