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

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

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

tangent of

f (x) = \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

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

\frac{d y}{d x} + 4 x y^{2} = 0

\int \frac{4 x ^{3}}{x ^{4} + 1} d x

\frac{( 2 t + 1 ) ^{\frac{3}{2}}}{3}

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

\frac{d}{d x} (6 (5 x^{2} + 2) x^{4} + 5)

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