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

The tangent of x/(-6x+6) is y= 1/(6(a_{0)-1)^2}x-(a_{0}^2)/(6(a_{0)-1)^2}

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tangent of x/(-6x+6)

tangent of

\frac{x}{- 6 x + 6}

y = \frac{1}{6 ( a _{0} - 1 ) ^{2}} x - \frac{a _{0}^{2}}{6 ( a _{0} - 1 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = \frac{x}{- 6 x + 6} : \frac{d y}{d x} = \frac{1}{6 ( x - 1 ) ^{2}}

Compute the slope of

y = \frac{x}{- 6 x + 6}

x = a_{0} : m = \frac{1}{6 ( a _{0} - 1 ) ^{2}}

Find the line with slope m=

\frac{1}{6 ( a _{0} - 1 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{- 6 a _{0} + 6}) : y = \frac{1}{6 ( a _{0} - 1 ) ^{2}} x - \frac{a _{0}^{2}}{6 ( a _{0} - 1 ) ^{2}}

y = \frac{1}{6 ( a _{0} - 1 ) ^{2}} x - \frac{a _{0}^{2}}{6 ( a _{0} - 1 ) ^{2}}

3 sin (x), 3 cos (x)

y^{^{'}} = t^{2} y^{3}

y^{^{'''}} - 3 y^{^{''}} - 9 y^{^{'}} + 27 y = 0

\frac{\partial}{\partial x} (2 x yz)

4 x + \frac{1}{x}

What is the tangent of x/(-6x+6) ?
The tangent of x/(-6x+6) is y= 1/(6(a_{0)-1)^2}x-(a_{0}^2)/(6(a_{0)-1)^2}