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

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

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tangent of x/(x+2)

tangent of

\frac{x}{x + 2}

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

Find the slope of

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

Find the line with slope m=

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

and passing through

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

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

\int x^{\frac{5}{3}} ln (x) d x

f (x) = x^{2} + 11 x - 15, at x = 1

\int 2 x^{3} \cdot cos (x^{2}) d x

\frac{d}{d x} (- 4 x - 3)

x y^{^{'}} + 2 y = 2 x^{2} - 3 x

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