MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{d}{{dx}}\left( {\frac{{{e^{{e^{{x^2}}}}} - e}}{x}} \right)$ is
- A$0$
- B$-e$
- ✓$e$
- D$e^2$
$\mathop {\lim }\limits_{x \to 0} \left( {2{e^{{x^2}}} \cdot {e^{{x^2}}} - \frac{{\left( {{e^{{e^{{x^2}}}}} - e} \right)}}{{{x^2}}}} \right)$
$ = 2e - \mathop {\lim }\limits_{x \to 0} \frac{{{\rm{e}}\left( {{{\rm{e}}^{{x^2} - 1}} - 1} \right)}}{{{{\rm{x}}^2}}}$
$=2 \mathrm{e}-\mathrm{e}=\mathrm{e}$
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