What is the tangent of (2x)/(x+1),\at x=1 ?

The tangent of (2x)/(x+1),\at x=1 is y= 1/2 x+1/2

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tangent of (2x)/(x+1),\at x=1

tangent of

\frac{2 x}{x + 1}, at x = 1

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

Solution steps

Find the tangent point:

(1, 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 = 1 : m = \frac{1}{2}

Find the line with slope m=

\frac{1}{2}

and passing through

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

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

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What is the tangent of (2x)/(x+1),\at x=1 ?
The tangent of (2x)/(x+1),\at x=1 is y= 1/2 x+1/2