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yn(x)=ex×ex2×ex3×…×exn \large y_n (x) = e^x \times e^{x^2} \times e^{x^3} \times \ldots \times e^{x^n} yn(x)=ex×ex2×ex3×…×exn
For some positive integer nnn, let yn(x)y_n(x) yn(x) denote function of xxx as stated above.
What is the value of the limit below?
limn→∞ddx(yn(x))∣x=12 \large \lim_{n\to\infty} \left . \frac d{dx} \left ( y_n (x) \right ) \right |_{x=\frac12} n→∞limdxd(yn(x))∣∣∣∣∣x=21
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