What is the derivative of y= x/(x^2+1) ?

The derivative of y= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)

What is the first derivative of y= x/(x^2+1) ?

The first derivative of y= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)

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derivative

\frac{- x ^{2} + 1}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) x}{( x ^{2} + 1 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 1) = 2 x

= \frac{1 \cdot ( x ^{2} + 1 ) - 2 xx}{( x ^{2} + 1 ) ^{2}}

1 \cdot (x^{2} + 1) - 2 xx = - x^{2} + 1

= \frac{- x ^{2} + 1}{( x ^{2} + 1 ) ^{2}}

What is the derivative of y= x/(x^2+1) ?
The derivative of y= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)
What is the first derivative of y= x/(x^2+1) ?
The first derivative of y= x/(x^2+1) is (-x^2+1)/((x^2+1)^2)