Differentiate the following functions with respect to x: 1+ 1- - Vidyadip

Question

Differentiate the following functions with respect to x:$\frac{1+\log\text{x}}{1-\log\text{x}}$

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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{1+\log\text{x}}{1-\log\text{x}}\Big)$
Using quotient rule, we get
$\frac{(1-\log\text{x})\frac{\text{d}}{\text{dx}}(1+\log\text{x})-(1+\log\text{x})\frac{\text{d}}{\text{dx}}(1-\log\text{x})}{(1-\log\text{x})^2}$
$\frac{(1-\log\text{x})\times\frac{1}{\text{x}}-(1+\log\text{x})\big(\frac{-1}{\text{x}}\big)}{(1-\log\text{x})^2}$
$=\frac{1-\log\text{x}+1+\log\text{x}}{\text{x}(1-\log\text{x})^2}$
$=\frac{2}{\text{x}(1-\log\text{x})^2}$

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