What is the tangent of ((x-10))/(5x+7) ?

The tangent of ((x-10))/(5x+7) is y=(57)/((5a_{0)+7)^2}x+(5a_{0}^2-100a_{0}-70)/((5a_{0)+7)^2}

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tangent of ((x-10))/(5x+7)

tangent of

\frac{( x - 10 )}{5 x + 7}

y = \frac{57}{( 5 a _{0} + 7 ) ^{2}} x + \frac{5 a _{0}^{2} - 100 a _{0} - 70}{( 5 a _{0} + 7 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0} - 10}{5 a _{0} + 7})

Find the slope of

y = \frac{x - 10}{5 x + 7} : \frac{d y}{d x} = \frac{57}{( 5 x + 7 ) ^{2}}

Compute the slope of

y = \frac{x - 10}{5 x + 7}

x = a_{0} : m = \frac{57}{( 5 a _{0} + 7 ) ^{2}}

Find the line with slope m=

\frac{57}{( 5 a _{0} + 7 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0} - 10}{5 a _{0} + 7}) : y = \frac{57}{( 5 a _{0} + 7 ) ^{2}} x + \frac{5 a _{0}^{2} - 100 a _{0} - 70}{( 5 a _{0} + 7 ) ^{2}}

y = \frac{57}{( 5 a _{0} + 7 ) ^{2}} x + \frac{5 a _{0}^{2} - 100 a _{0} - 70}{( 5 a _{0} + 7 ) ^{2}}

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What is the tangent of ((x-10))/(5x+7) ?
The tangent of ((x-10))/(5x+7) is y=(57)/((5a_{0)+7)^2}x+(5a_{0}^2-100a_{0}-70)/((5a_{0)+7)^2}