What is the tangent of (x^2)/(x-6) ?

The tangent of (x^2)/(x-6) is y=(a_{0}^2-12a_{0})/((a_{0)-6)^2}x+(6a_{0}^2)/((a_{0)-6)^2}

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tangent of (x^2)/(x-6)

tangent of

\frac{x ^{2}}{x - 6}

y = \frac{a _{0}^{2} - 12 a _{0}}{( a _{0} - 6 ) ^{2}} x + \frac{6 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}^{2}}{a _{0} - 6})

Find the slope of

y = \frac{x ^{2}}{x - 6} : \frac{d y}{d x} = \frac{x ^{2} - 12 x}{( x - 6 ) ^{2}}

Compute the slope of

y = \frac{x ^{2}}{x - 6}

x = a_{0} : m = \frac{a _{0}^{2} - 12 a _{0}}{( a _{0} - 6 ) ^{2}}

Find the line with slope m=

\frac{a _{0}^{2} - 12 a _{0}}{( a _{0} - 6 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}^{2}}{a _{0} - 6}) : y = \frac{a _{0}^{2} - 12 a _{0}}{( a _{0} - 6 ) ^{2}} x + \frac{6 a _{0}^{2}}{( a _{0} - 6 ) ^{2}}

y = \frac{a _{0}^{2} - 12 a _{0}}{( a _{0} - 6 ) ^{2}} x + \frac{6 a _{0}^{2}}{( a _{0} - 6 ) ^{2}}

\frac{d}{d x} (\frac{2 cos ( 2 x ) - 1}{2 cos ( x )})

\frac{\partial}{\partial y} (1 + e^{x} y + x e^{x} y)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 4} e^{3 t}

f (x) = (2 x - 8)^{5}

2 x^{3} + 4 x^{2} - 5 x - 3

What is the tangent of (x^2)/(x-6) ?
The tangent of (x^2)/(x-6) is y=(a_{0}^2-12a_{0})/((a_{0)-6)^2}x+(6a_{0}^2)/((a_{0)-6)^2}