` = e^(x ^(3))`

Explanation

To differentiate the function \( y = e^{x^3} \), we will follow the steps of differentiation using the chain rule.

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( y = e^{x^3} \).

2. **Apply the chain rule**: The chain rule states that if you have a composite function \( y = e^{u} \) where \( u = x^3 \), then the derivative \( \frac{dy}{dx} \) is given by:
\[
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