If y= 1+1 x^2 1-1 x^2 , then d y d x is equal to ________________… - Vidyadip

Question

If $y=\frac{1+\frac{1}{x^2}}{1-\frac{1}{x^2}}$, then $\frac{d y}{d x}$ is equal to _________________

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Answer

$\frac{-4 x}{\left(x^2-1\right)^2}$, because,
Given,
$y=\frac{1+\frac{1}{x^2}}{1-\frac{1}{x^2}} \Rightarrow \frac{x^2+1}{x^2-1}$
$\frac{d y}{d x}=\frac{\left(x^2-1\right) \cdot 2 x-\left(x^2+1\right) \cdot 2 x}{\left(x^2-1\right)^2}$
$=\frac{2 x\left(x^2-1-x^2-1\right)}{\left(x^2-1\right)^2}$
$\begin{array}{l}=\frac{2 x(-2)}{\left(x^2-1\right)^2} \\ =\frac{-4 x}{\left(x^2-1\right)^2}\end{array}$

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