Differentiate the following w.r.t. x:

Let $y=e^{x^{3}}$

By using the chain rule, we obtain

$\frac{d y}{d x}=\frac{d}{d x}\left(e^{x^{3}}\right)=e^{x^{3}} \cdot \frac{d}{d x}\left(x^{3}\right)=e^{x^{3}} \cdot 3 x^{2}=3 x^{2} e^{x^{3}}$