Given y=x ex, find dydx and d2ydx2. Hence find the value of the second derivative at x=0. At x=0, fi

Question

Given y=x ex, find dydx and d2ydx2. Hence find the value of the second derivative at x=0. At x=0, find the ratio of the second derivative to the first derivative.

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=x e^{x} + e^{x}$; $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=\left(x + 2\right) e^{x}$; at $x=0$, $2$. The ratio is $2$.

Second derivatives

Second derivatives

Solution:

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