What is the tangent of (6x)/(x+5) ?

The tangent of (6x)/(x+5) is y=(30)/((a_{0)+5)^2}x+(6a_{0}^2)/((a_{0)+5)^2}

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tangent of (6x)/(x+5)

tangent of

\frac{6 x}{x + 5}

y = \frac{30}{( a _{0} + 5 ) ^{2}} x + \frac{6 a _{0}^{2}}{( a _{0} + 5 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{6 a _{0}}{a _{0} + 5})

Find the slope of

y = \frac{6 x}{x + 5} : \frac{d y}{d x} = \frac{30}{( x + 5 ) ^{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{30}{( a _{0} + 5 ) ^{2}}

Find the line with slope m=

\frac{30}{( a _{0} + 5 ) ^{2}}

and passing through

(a_{0}, \frac{6 a _{0}}{a _{0} + 5}) : y = \frac{30}{( a _{0} + 5 ) ^{2}} x + \frac{6 a _{0}^{2}}{( a _{0} + 5 ) ^{2}}

y = \frac{30}{( a _{0} + 5 ) ^{2}} x + \frac{6 a _{0}^{2}}{( a _{0} + 5 ) ^{2}}

What is the tangent of (6x)/(x+5) ?
The tangent of (6x)/(x+5) is y=(30)/((a_{0)+5)^2}x+(6a_{0}^2)/((a_{0)+5)^2}