What is the tangent of 6/(x-1) ?

The tangent of 6/(x-1) is y=-6/((a_{0)-1)^2}x+(12a_{0}-6)/((a_{0)-1)^2}

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tangent of 6/(x-1)

tangent of

\frac{6}{x - 1}

y = - \frac{6}{( a _{0} - 1 ) ^{2}} x + \frac{12 a _{0} - 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{6}{a _{0} - 1})

Find the slope of

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

Find the line with slope m=

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

and passing through

(a_{0}, \frac{6}{a _{0} - 1}) : y = - \frac{6}{( a _{0} - 1 ) ^{2}} x + \frac{12 a _{0} - 6}{( a _{0} - 1 ) ^{2}}

y = - \frac{6}{( a _{0} - 1 ) ^{2}} x + \frac{12 a _{0} - 6}{( a _{0} - 1 ) ^{2}}

\frac{d}{d x} (2 (x^{3} - x)^{4})

\frac{d}{d x} (x^{2} - x y + y^{2})

\int_{0}^{1} \frac{63}{4 y - 1} d y

e^{x} (3 x^{2} - 6 x + 6)

x \to 0 - lim (7 - 2 x)

What is the tangent of 6/(x-1) ?
The tangent of 6/(x-1) is y=-6/((a_{0)-1)^2}x+(12a_{0}-6)/((a_{0)-1)^2}