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Logarithmic Differentiation

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Question

differentiate
$y = l o g ({3 x}^{2} + 2 x + 1)$

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Solution

$y = log (3 x^{2} + 2 x + 1)$
$\Rightarrow \frac{d y}{d x} = \frac{1}{(3 x^{2} + 2 x + 1)} \frac{d}{d x} (3 x^{2} + 2 x + 1)$
$\Rightarrow \frac{d y}{d x} = \frac{1}{(3 x^{2} + 2 x + 1)} (6 x + 2)$
$∴ \frac{d y}{d x} = \frac{2 (3 x + 1)}{(3 x^{2} + 2 x + 1)}$

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