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}}

Compute the slope of

y = \frac{6 x}{x + 5}

x = a_{0} : 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}}

f (x) = 2 x^{2} - 6 x + 4

\int e^{(- s + 4) t} t d t

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

\int e^{(- 3 x)} d x

\int_{0}^{1} (x^{6} + x^{8}) d x

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}