What is the tangent of (5x)/(x+4) ?

The tangent of (5x)/(x+4) is y=(20)/((a_{0)+4)^2}x+(5a_{0}^2)/((a_{0)+4)^2}

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tangent of (5x)/(x+4)

tangent of

\frac{5 x}{x + 4}

y = \frac{20}{( a _{0} + 4 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 4 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{5 a _{0}}{a _{0} + 4})

Find the slope of

y = \frac{5 x}{x + 4} : \frac{d y}{d x} = \frac{20}{( x + 4 ) ^{2}}

Compute the slope of

y = \frac{5 x}{x + 4}

x = a_{0} : m = \frac{20}{( a _{0} + 4 ) ^{2}}

Find the line with slope m=

\frac{20}{( a _{0} + 4 ) ^{2}}

and passing through

(a_{0}, \frac{5 a _{0}}{a _{0} + 4}) : y = \frac{20}{( a _{0} + 4 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 4 ) ^{2}}

y = \frac{20}{( a _{0} + 4 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 4 ) ^{2}}

\frac{d}{d x} (\frac{3}{tan ( x )})

x \to 1 lim (\frac{∣ x + 1 ∣}{x + 1})

\frac{\partial}{\partial y} (ln (x) y)

\int y - \frac{1}{y ^{2}} d y

What is the tangent of (5x)/(x+4) ?
The tangent of (5x)/(x+4) is y=(20)/((a_{0)+4)^2}x+(5a_{0}^2)/((a_{0)+4)^2}