What is the tangent of x/((x+1)) ?

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

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tangent of x/((x+1))

tangent of

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

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

Find the slope of

y = \frac{x}{x + 1} : \frac{d y}{d x} = \frac{1}{( x + 1 ) ^{2}}

Compute the slope of

y = \frac{x}{x + 1}

x = a_{0} : m = \frac{1}{( a _{0} + 1 ) ^{2}}

Find the line with slope m=

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

and passing through

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

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

\int (x^{2} + 4)^{\frac{1}{2}} d x

\int_{0}^{y} 0.125 d x

x \to 1 lim (x^{(\frac{1}{1 - x})})

n = 1 \sum \infty n^{2} (\frac{2}{3})^{n}

\frac{d}{d x} (7 x - 1)

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