What is the tangent of (-4x)/(x^2+1) ?

The tangent of (-4x)/(x^2+1) is y=-(4(-a_{0}^2+1))/((a_{0)^2+1)^2}x-(8a_{0}^3)/((a_{0)^2+1)^2}

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tangent of (-4x)/(x^2+1)

tangent of

\frac{- 4 x}{x ^{2} + 1}

y = - \frac{4 ( - a _{0}^{2} + 1 )}{( a _{0}^{2} + 1 ) ^{2}} x - \frac{8 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{4 a _{0}}{a _{0}^{2} + 1})

Find the slope of

y = \frac{- 4 x}{x ^{2} + 1} : \frac{d y}{d x} = - \frac{4 ( - 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{4 ( - a _{0}^{2} + 1 )}{( a _{0}^{2} + 1 ) ^{2}}

Find the line with slope m=

- \frac{4 ( - a _{0}^{2} + 1 )}{( a _{0}^{2} + 1 ) ^{2}}

and passing through

(a_{0}, - \frac{4 a _{0}}{a _{0}^{2} + 1}) : y = - \frac{4 ( - a _{0}^{2} + 1 )}{( a _{0}^{2} + 1 ) ^{2}} x - \frac{8 a _{0}^{3}}{( a _{0}^{2} + 1 ) ^{2}}

y = - \frac{4 ( - a _{0}^{2} + 1 )}{( a _{0}^{2} + 1 ) ^{2}} x - \frac{8 a _{0}^{3}}{( a _{0}^{2} + 1 ) ^{2}}

\frac{d}{d x} ((x - 4)^{2})

\int \frac{( 1 - x ) ^{3}}{x ^{3} x} d x

\frac{d}{d t} (e^{3 t} cos (2 t))

f (x) = ln (4 - x^{8})

\frac{d ^{2} y}{d x ^{2}} - 49 \frac{d y}{d x} = e^{7 x}

What is the tangent of (-4x)/(x^2+1) ?
The tangent of (-4x)/(x^2+1) is y=-(4(-a_{0}^2+1))/((a_{0)^2+1)^2}x-(8a_{0}^3)/((a_{0)^2+1)^2}