What is the tangent of-1/((x-6)^2) ?

The tangent of-1/((x-6)^2) is y= 2/((a_{0)-6)^3}x+(-3a_{0}+6)/((a_{0)-6)^3}

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tangent of-1/((x-6)^2)

tangent of

- \frac{1}{( x - 6 ) ^{2}}

y = \frac{2}{( a _{0} - 6 ) ^{3}} x + \frac{- 3 a _{0} + 6}{( a _{0} - 6 ) ^{3}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = - \frac{1}{( x - 6 ) ^{2}} : \frac{d y}{d x} = \frac{2}{( x - 6 ) ^{3}}

Compute the slope of

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

x = a_{0} : m = \frac{2}{( a _{0} - 6 ) ^{3}}

Find the line with slope m=

\frac{2}{( a _{0} - 6 ) ^{3}}

and passing through

(a_{0}, - \frac{1}{( a _{0} - 6 ) ^{2}}) : y = \frac{2}{( a _{0} - 6 ) ^{3}} x + \frac{- 3 a _{0} + 6}{( a _{0} - 6 ) ^{3}}

y = \frac{2}{( a _{0} - 6 ) ^{3}} x + \frac{- 3 a _{0} + 6}{( a _{0} - 6 ) ^{3}}

\int csc (4 x) d x

\frac{d}{d x} (arcsinh (x))

\int - \frac{4}{x ^{2}} d x

\frac{d y}{d x} = \frac{y}{y ^{2}}, y (0) = 2

What is the tangent of-1/((x-6)^2) ?
The tangent of-1/((x-6)^2) is y= 2/((a_{0)-6)^3}x+(-3a_{0}+6)/((a_{0)-6)^3}