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

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

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tangent of y= x/(x+1)

tangent of

y = \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}}

y^{^{'''}} + 5 y^{^{''}} = 0

\int_{0}^{1} (x - x^{2}) d x

\frac{d}{d x} (- \frac{1}{2 ^{x}})

\frac{\partial}{\partial x} (1 0^{x})

\frac{x ^{2} - 2 x + 3}{x + 1}

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