Exponentiated Geometric Sum

Calculus Level 2

$\large y_n (x) = e^x \times e^{x^2} \times e^{x^3} \times \ldots \times e^{x^n}$

For some positive integer $n$, let $y_n(x)$ denote function of $x$ as stated above.

What is the value of the limit below?

$\large \lim_{n\to\infty} \left . \frac d{dx} \left ( y_n (x) \right ) \right |_{x=\frac12}$

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