What is the tangent of x/(x+6) ?

The tangent of x/(x+6) is y= 6/((a_{0)+6)^2}x+(a_{0}^2)/((a_{0)+6)^2}

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tangent of x/(x+6)

tangent of

\frac{x}{x + 6}

y = \frac{6}{( a _{0} + 6 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} + 6 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{a _{0} + 6})

Find the slope of

y = \frac{x}{x + 6} : \frac{d y}{d x} = \frac{6}{( x + 6 ) ^{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{6}{( a _{0} + 6 ) ^{2}}

Find the line with slope m=

\frac{6}{( a _{0} + 6 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0} + 6}) : y = \frac{6}{( a _{0} + 6 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} + 6 ) ^{2}}

y = \frac{6}{( a _{0} + 6 ) ^{2}} x + \frac{a _{0}^{2}}{( a _{0} + 6 ) ^{2}}

\int \frac{x ^{2} - 1}{x ( x + 1 ) ^{3}} d x

x \to 0 lim (\frac{5 x ^{2}}{x ^{2}})

\int_{- 1}^{1} π (1 - x^{2})^{2} d x

f (t) = (4 t^{2} + 5)

f (x) = 4 t - 4 e^{t}

What is the tangent of x/(x+6) ?
The tangent of x/(x+6) is y= 6/((a_{0)+6)^2}x+(a_{0}^2)/((a_{0)+6)^2}