What is the tangent of f(x)= x/(x^2+81) ?

The tangent of f(x)= x/(x^2+81) is y=(-a_{0}^2+81)/((a_{0)^2+81)^2}x+(2a_{0}^3)/((a_{0)^2+81)^2}

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tangent of f(x)= x/(x^2+81)

tangent of

f (x) = \frac{x}{x ^{2} + 81}

y = \frac{- a _{0}^{2} + 81}{( a _{0}^{2} + 81 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 81 ) ^{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} + 81})

Find the slope of

f (x) = \frac{x}{x ^{2} + 81} : \frac{df ( x )}{d x} = \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{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} + 81}{( a _{0}^{2} + 81 ) ^{2}}

Find the line with slope m=

\frac{- a _{0}^{2} + 81}{( a _{0}^{2} + 81 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 81}) : y = \frac{- a _{0}^{2} + 81}{( a _{0}^{2} + 81 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 81 ) ^{2}}

y = \frac{- a _{0}^{2} + 81}{( a _{0}^{2} + 81 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 81 ) ^{2}}

x = 2 y^{2} - 5, x = y^{2} + 4

y = 2 x - 5

\int x^{- 12} d x

f (x) = 6 x^{3} - 9 x + 4

\frac{x + 1}{x + 4}

What is the tangent of f(x)= x/(x^2+81) ?
The tangent of f(x)= x/(x^2+81) is y=(-a_{0}^2+81)/((a_{0)^2+81)^2}x+(2a_{0}^3)/((a_{0)^2+81)^2}