What is the tangent of 2/(4-x) ?

The tangent of 2/(4-x) is y= 2/((4-a_{0))^2}x+(-4a_{0}+8)/((-a_{0)+4)^2}

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tangent of 2/(4-x)

tangent of

\frac{2}{4 - x}

y = \frac{2}{( 4 - a _{0} ) ^{2}} x + \frac{- 4 a _{0} + 8}{( - a _{0} + 4 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{4 - a _{0}})

Find the slope of

y = \frac{2}{4 - x} : \frac{d y}{d x} = \frac{2}{( 4 - x ) ^{2}}

Compute the slope of

y = \frac{2}{4 - x}

x = a_{0} : m = \frac{2}{( 4 - a _{0} ) ^{2}}

Find the line with slope m=

\frac{2}{( 4 - a _{0} ) ^{2}}

and passing through

(a_{0}, \frac{2}{4 - a _{0}}) : y = \frac{2}{( 4 - a _{0} ) ^{2}} x + \frac{- 4 a _{0} + 8}{( - a _{0} + 4 ) ^{2}}

y = \frac{2}{( 4 - a _{0} ) ^{2}} x + \frac{- 4 a _{0} + 8}{( - a _{0} + 4 ) ^{2}}

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What is the tangent of 2/(4-x) ?
The tangent of 2/(4-x) is y= 2/((4-a_{0))^2}x+(-4a_{0}+8)/((-a_{0)+4)^2}