If y= _ax,, find dy dx . - Vidyadip

Question

If $\text{y}=\log_\text{a}\text{x},$, find $\frac{\text{dy}}{\text{dx}}.$

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Answer

We have, $\text{y}=\log_\text{a}\text{x},$
$\Rightarrow\text{y}=\frac{\log\text{x}}{\log\text{a}} \Big[\because\log_\text{a}\text{b}=\frac{\log\text{b}}{\log\text{a}}\Big]$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\log\text{a}}\frac{\text{d}}{\text{dx}}(\log\text{x})$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\log\text{a}}\Big(\frac{1}{\text{x}}\Big)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}\log\text{a}}$

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