What is the tangent of (4x)/(x+1) ?

The tangent of (4x)/(x+1) is y= 4/((a_{0)+1)^2}x+(4a_{0}^2)/((a_{0)+1)^2}

tangent of (4x)/(x+1)

tangent of

\frac{4 x}{x + 1}

y = \frac{4}{( a _{0} + 1 ) ^{2}} x + \frac{4 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{4 a _{0}}{a _{0} + 1})

Find the slope of

y = \frac{4 x}{x + 1} : \frac{d y}{d x} = \frac{4}{( 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{4}{( a _{0} + 1 ) ^{2}}

Find the line with slope m=

\frac{4}{( a _{0} + 1 ) ^{2}}

and passing through

(a_{0}, \frac{4 a _{0}}{a _{0} + 1}) : y = \frac{4}{( a _{0} + 1 ) ^{2}} x + \frac{4 a _{0}^{2}}{( a _{0} + 1 ) ^{2}}

y = \frac{4}{( a _{0} + 1 ) ^{2}} x + \frac{4 a _{0}^{2}}{( a _{0} + 1 ) ^{2}}

\int_{1}^{1.5} (\frac{1}{8} + \frac{3}{8} x) d x

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

\int_{0}^{π} 11 sin^{2} (2 x) d x

d er i v a t i v e y = ln (8 x^{2} - 7 x + 9)

d er i v a t i v e f (t) = e^{9 t s i n (2 t)}

What is the tangent of (4x)/(x+1) ?
The tangent of (4x)/(x+1) is y= 4/((a_{0)+1)^2}x+(4a_{0}^2)/((a_{0)+1)^2}