What is the tangent of (2x)/(x+1) ?

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

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tangent of (2x)/(x+1)

tangent of

\frac{2 x}{x + 1}

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

Find the slope of

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

Compute the slope of

y = \frac{2 x}{x + 1}

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

Find the line with slope m=

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

and passing through

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

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

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

\frac{\partial}{\partial x} (5 y cos (6 x))

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

e^{- x} x^{2} + 3 e^{- x} - e^{- x}

x y^{^{'}} + y + x = 0, y (1) = 1

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