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If $\mathrm{y}=\mathrm{e}^{\mathrm{x}^{2}} \sin 2 \mathrm{x}$, then what is $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{x}=\pi$ equal to?
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Verified Answer
The correct answer is:
$2 \mathrm{e}^{\pi^{2}}$
$y=e^{x^{2}} \cdot \sin 2 x$
$\frac{d y}{d x}=2 \cdot e^{x^{2}} \cdot \cos 2 x+2 x e^{x^{2}} \cdot \sin 2 x$
$=2 e^{x^{2}}(\cos 2 x+x \sin 2 x)$
$\left.\frac{d y}{d x}\right|_{x=\pi}=2 e^{\pi^{2}}(\cos 2 \pi+\pi \cdot \sin 2 \pi)$
$=2 e^{\pi^{2}}(1+0)$
$=2 \cdot e^{\pi^{2}}$
$\frac{d y}{d x}=2 \cdot e^{x^{2}} \cdot \cos 2 x+2 x e^{x^{2}} \cdot \sin 2 x$
$=2 e^{x^{2}}(\cos 2 x+x \sin 2 x)$
$\left.\frac{d y}{d x}\right|_{x=\pi}=2 e^{\pi^{2}}(\cos 2 \pi+\pi \cdot \sin 2 \pi)$
$=2 e^{\pi^{2}}(1+0)$
$=2 \cdot e^{\pi^{2}}$
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