Using the chain rule, we have:
$$\frac{dy}{du} = e^u$$
Now, we need to find the derivative of $y = e^{x^2}$ with respect to $x$. Let $u = x^2$. Then, $y = e^u$. We need to find $\frac{dy}{dx}$.
Using the chain rule, we have:
$$\frac{dy}{dx} = \frac{dy}{du}
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