What is the slope of x/(x^2+1) ?

The slope of x/(x^2+1) is (-x^2+1)/((x^2+1)^2)

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slope of x/(x^2+1)

slope

\frac{x}{x ^{2} + 1}

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

Solution steps

y = \frac{x}{x ^{2} + 1}

In order to find the slope of the function, take the derivative of

\frac{x}{x ^{2} + 1}

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

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

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0, y (0) = 8

\int (x + 6)^{4} d x

y = x, y = x, x = 0, x = 2

f (x) = x x^{2} + 1

(t^{2} - 1)^{2}