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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of x/(x^2+81)

tangent of

\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

y = \frac{x}{x ^{2} + 81} : \frac{d y}{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}}

\frac{\partial}{\partial y} (x e^{x^{3} y})

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

\frac{\partial}{\partial x} (\frac{- 2 x - y}{( x - y ) ^{4}})

\int x \cdot ln (\frac{1}{x}) d x

\int \frac{1 - e ^{- 4 x}}{1 + e ^{- 4 x}} d x

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