Question
Differentiate the following functions with respect to x:
$\frac{\text{2x}-1}{\text{x}^2+1}$
$\frac{\text{2x}-1}{\text{x}^2+1}$
$=\frac{(\text{x}^2+1)\times2-(\text{2x}-1)\times\text{2x}}{(\text{x}^2+1)^2}$
$=\frac{\text{2x}^2+2-\text{4x}^2+\text{2x}}{(\text{x}^2+1)^2}$
$=\frac{-\text{2x}+\text{2x}+2}{(\text{x}^2+1)^2}$
$=\frac{2(-\text{x}^2+\text{x}+1)}{(\text{x}^2+1)^2}$
$=\frac{2(1+\text{x}-\text{x}^2)}{(\text{x}^2+1)^2}$
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