Example $1.$ Find $f^{\text{'}}(x)$ for each function using the derivative of $e^x$ and product$/$quotient rules as needed. Watch out for expressions with $e$ that are constants $-$ not functions.

$($a$)f(x)=e^{x}x$

$($b$)f(x)=4e^{x}e{x}^e$

Watch Out! Is $x^e$ an exponential function?

$($c$)f(x)=e^3-3e^x-6e^3$

$($d$)f(x)=x{e}^x$

Revorite: $f(x)=(x)(e^x)$ Product Robe!