What is the tangent of y= 1/(x-1),\at x=6 ?

The tangent of y= 1/(x-1),\at x=6 is y=-1/25 x+11/25

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tangent of y= 1/(x-1),\at x=6

tangent of

y = \frac{1}{x - 1}, at x = 6

y = - \frac{1}{25} x + \frac{11}{25}

Solution steps

Find the tangent point:

(6, \frac{1}{5})

Find the slope of

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

Compute the slope of

y = \frac{1}{x - 1}

x = 6 : m = - \frac{1}{25}

Find the line with slope m=

- \frac{1}{25}

and passing through

(6, \frac{1}{5}) : y = - \frac{1}{25} x + \frac{11}{25}

y = - \frac{1}{25} x + \frac{11}{25}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0

\frac{d}{d x} (- 10 sin (2 x + 10))

y^{^{''}} + 25 y = - 20 sin (5 t)

\frac{d}{d x} (3 cos (3 x + 1))

What is the tangent of y= 1/(x-1),\at x=6 ?
The tangent of y= 1/(x-1),\at x=6 is y=-1/25 x+11/25