If y= |3x|,x 0, find dy dx . - Vidyadip

Question

If $\text{y}=\log|3\text{x}|,\text{x}\neq0,$ find $\frac{\text{dy}}{\text{dx}}.$

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Answer

We have, $\text{y}=\log|3\text{x}|$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}(\log|3\text{x}|)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{3\text{x}}\frac{\text{d}}{\text{dx}}(3\text{x})$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{3\text{x}}(3)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$

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