Find the second order derivatives of $x^{2} + 3 x + 2$

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Solution

Let $y = x^{2} + 3 x + 2$
$\Rightarrow \frac{d y}{d x} = \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 x) + \frac{d}{d x} (2) = 2 x + 3 + 0 = 2 x + 3$
$∴ \frac{d^{2} y}{d x^{2}} = \frac{d}{d x} (2 x + 3) = \frac{d}{d x} (2 x) + \frac{d}{d x} (3) = 2 + 0 = 2$

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