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

The tangent of y=(2x+1)/(x+2) is y= 3/((a_{0)+2)^2}x+(2a_{0}^2+2a_{0}+2)/((a_{0)+2)^2}

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

tangent of

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

y = \frac{3}{( a _{0} + 2 ) ^{2}} x + \frac{2 a _{0}^{2} + 2 a _{0} + 2}{( a _{0} + 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = \frac{2 x + 1}{x + 2} : \frac{d y}{d x} = \frac{3}{( x + 2 ) ^{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{3}{( a _{0} + 2 ) ^{2}}

Find the line with slope m=

\frac{3}{( a _{0} + 2 ) ^{2}}

and passing through

(a_{0}, \frac{2 a _{0} + 1}{a _{0} + 2}) : y = \frac{3}{( a _{0} + 2 ) ^{2}} x + \frac{2 a _{0}^{2} + 2 a _{0} + 2}{( a _{0} + 2 ) ^{2}}

y = \frac{3}{( a _{0} + 2 ) ^{2}} x + \frac{2 a _{0}^{2} + 2 a _{0} + 2}{( a _{0} + 2 ) ^{2}}

\int e^{- s t} sin (2 t) d t

\frac{d}{d x} (tanh (e^{x}))

\frac{10}{s \cdot ( s + 5 ) ^{2}}

\int_{0}^{4} 3 2 x d x

\frac{x ^{2} - 4 x + 3}{x ^{2}}

What is the tangent of y=(2x+1)/(x+2) ?
The tangent of y=(2x+1)/(x+2) is y= 3/((a_{0)+2)^2}x+(2a_{0}^2+2a_{0}+2)/((a_{0)+2)^2}