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

The tangent of y= 2/(x-6) is y=-2/((a_{0)-6)^2}x+(4a_{0}-12)/((a_{0)-6)^2}

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tangent of y= 2/(x-6)

tangent of

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

y = - \frac{2}{( a _{0} - 6 ) ^{2}} x + \frac{4 a _{0} - 12}{( a _{0} - 6 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 6})

Find the slope of

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

Compute the slope of

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

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

Find the line with slope m=

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

and passing through

(a_{0}, \frac{2}{a _{0} - 6}) : y = - \frac{2}{( a _{0} - 6 ) ^{2}} x + \frac{4 a _{0} - 12}{( a _{0} - 6 ) ^{2}}

y = - \frac{2}{( a _{0} - 6 ) ^{2}} x + \frac{4 a _{0} - 12}{( a _{0} - 6 ) ^{2}}

y = - 3 x

\int (- x^{8} + 4)^{6} x^{7} d x

y = - \frac{2 x ^{2}}{5 y ^{2}}

\frac{d}{d x} (8 e^{8 x})

sin (x) \cdot e^{x}

What is the tangent of y= 2/(x-6) ?
The tangent of y= 2/(x-6) is y=-2/((a_{0)-6)^2}x+(4a_{0}-12)/((a_{0)-6)^2}