What is the tangent of x/(x^2+25) ?

The tangent of x/(x^2+25) is y=(-a_{0}^2+25)/((a_{0)^2+25)^2}x+(2a_{0}^3)/((a_{0)^2+25)^2}

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tangent of x/(x^2+25)

tangent of

\frac{x}{x ^{2} + 25}

y = \frac{- a _{0}^{2} + 25}{( a _{0}^{2} + 25 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 25 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 25})

Find the slope of

y = \frac{x}{x ^{2} + 25} : \frac{d y}{d x} = \frac{- x ^{2} + 25}{( x ^{2} + 25 ) ^{2}}

Compute the slope of

y = \frac{x}{x ^{2} + 25}

x = a_{0} : m = \frac{- a _{0}^{2} + 25}{( a _{0}^{2} + 25 ) ^{2}}

Find the line with slope m=

\frac{- a _{0}^{2} + 25}{( a _{0}^{2} + 25 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 25}) : y = \frac{- a _{0}^{2} + 25}{( a _{0}^{2} + 25 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 25 ) ^{2}}

y = \frac{- a _{0}^{2} + 25}{( a _{0}^{2} + 25 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 25 ) ^{2}}

\frac{d}{d x} (arctan (a x))

\int (2 x^{- 3}) d x

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

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

4 x, 4 x - x^{2}, 0, 2

What is the tangent of x/(x^2+25) ?
The tangent of x/(x^2+25) is y=(-a_{0}^2+25)/((a_{0)^2+25)^2}x+(2a_{0}^3)/((a_{0)^2+25)^2}