What is the tangent of (5x)/(x+3) ?

The tangent of (5x)/(x+3) is y=(15)/((a_{0)+3)^2}x+(5a_{0}^2)/((a_{0)+3)^2}

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tangent of (5x)/(x+3)

tangent of

\frac{5 x}{x + 3}

y = \frac{15}{( a _{0} + 3 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 3 ) ^{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} + 3})

Find the slope of

y = \frac{5 x}{x + 3} : \frac{d y}{d x} = \frac{15}{( x + 3 ) ^{2}}

Compute the slope of

y = \frac{5 x}{x + 3}

x = a_{0} : m = \frac{15}{( a _{0} + 3 ) ^{2}}

Find the line with slope m=

\frac{15}{( a _{0} + 3 ) ^{2}}

and passing through

(a_{0}, \frac{5 a _{0}}{a _{0} + 3}) : y = \frac{15}{( a _{0} + 3 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

y = \frac{15}{( a _{0} + 3 ) ^{2}} x + \frac{5 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

\int 2 + x d x

\frac{d}{d x} (\frac{25 - x ^{2}}{16 x})

\frac{\partial ^{2}}{\partial x \partial y} (1 + x y^{2})

\int_{2}^{11} (x - 3)^{- \frac{2}{3}} d x

f (x) = arcsin (3 x)

What is the tangent of (5x)/(x+3) ?
The tangent of (5x)/(x+3) is y=(15)/((a_{0)+3)^2}x+(5a_{0}^2)/((a_{0)+3)^2}