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Algebra of Derivatives

Find the deri...

Question

Find the derivative of $y = e^{x} (x^{2} - 2 x + 2)$

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Solution

$y = e^{x} (x^{2} - 2 x + 2)$

Applying product Rule of differentiation
$\frac{d y}{d x} = e^{x} \cdot \frac{d}{d x} (x^{2} - 2 x + 2) + (x^{2} - 2 x + 2) \frac{d}{d x} (e^{x})$

$= e^{x} (2 x - 2) + (x^{2} - 2 x + 2) e^{x}$

$= 2 x e^{x} - 2 e^{x} + x^{2} e^{x} - 2 x e^{x} + 2 e^{x}$

$= x^{2} e^{x}$ .

$\frac{d y}{d x} = x^{2} e^{x}$ .

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