Answer
$y' = 3{e^x} - \frac{4}{3}{x^{ - 4/3}}$
Work Step by Step
$$\eqalign{
& y = 3{e^x} + \frac{4}{{\root 3 \of x }} \cr
& {\text{Rewrite the function}} \cr
& y = 3{e^x} + 4{x^{ - 1/3}} \cr
& {\text{Differentiate}} \cr
& y' = \frac{d}{{dx}}\left[ {3{e^x}} \right] + \frac{d}{{dx}}\left[ {4{x^{ - 1/3}}} \right] \cr
& {\text{Use the constant multiple rule}} \cr
& y' = 3\frac{d}{{dx}}\left[ {{e^x}} \right] + 4\frac{d}{{dx}}\left[ {{x^{ - 1/3}}} \right] \cr
& {\text{Apply the power rule: }}\frac{d}{{dx}}\left[ {{x^n}} \right] = n{x^{n - 1}}{\text{ and }}\frac{d}{{dx}}\left[ {{e^x}} \right] = {e^x} \cr
& y' = 3\left( {{e^x}} \right) + 4\left( { - \frac{1}{3}{x^{ - 4/3}}} \right) \cr
& y' = 3{e^x} - \frac{4}{3}{x^{ - 4/3}} \cr} $$
