What is the tangent of f(x)= x/(x^2+1) ?

The tangent of f(x)= x/(x^2+1) is y=(-a_{0}^2+1)/((a_{0)^2+1)^2}x+(2a_{0}^3)/((a_{0)^2+1)^2}

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tangent of f(x)= x/(x^2+1)

tangent of

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

y = \frac{- a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 1 ) ^{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} + 1})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{- a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}}

Find the line with slope m=

\frac{- a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 1}) : y = \frac{- a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 1 ) ^{2}}

y = \frac{- a _{0}^{2} + 1}{( a _{0}^{2} + 1 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

\frac{d y}{d x}, y - 5 x y^{3} + 8 = 5 sin (y^{3} + 2 x^{2})

\frac{\partial}{\partial x} (x (y + 1))

\int_{0}^{2 π} sin^{4} (x) d x

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

What is the tangent of f(x)= x/(x^2+1) ?
The tangent of f(x)= x/(x^2+1) is y=(-a_{0}^2+1)/((a_{0)^2+1)^2}x+(2a_{0}^3)/((a_{0)^2+1)^2}