What is the tangent of (4x)/(x+3)(1.1) ?

The tangent of (4x)/(x+3)(1.1) is y=(13.2)/((a_{0)+3)^2}x+(4.4a_{0}^2)/((a_{0)+3)^2}

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tangent of (4x)/(x+3)(1.1)

tangent of

\frac{4 x}{x + 3} (1.1)

y = \frac{13.2}{( a _{0} + 3 ) ^{2}} x + \frac{4.4 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{4.4 a _{0}}{a _{0} + 3})

Find the slope of

y = \frac{4 x}{x + 3} 1.1 : \frac{d y}{d x} = \frac{13.2}{( x + 3 ) ^{2}}

Compute the slope of

y = \frac{4 x}{x + 3} 1.1

x = a_{0} : m = \frac{13.2}{( a _{0} + 3 ) ^{2}}

Find the line with slope m=

\frac{13.2}{( a _{0} + 3 ) ^{2}}

and passing through

(a_{0}, \frac{4.4 a _{0}}{a _{0} + 3}) : y = \frac{13.2}{( a _{0} + 3 ) ^{2}} x + \frac{4.4 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

y = \frac{13.2}{( a _{0} + 3 ) ^{2}} x + \frac{4.4 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

n = 0 \sum \infty e^{- 4 n}

y = \frac{x ^{6}}{2 - x ^{5}}

\frac{1}{e ^{x} - 1}

\frac{1}{2 x + 1}

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

What is the tangent of (4x)/(x+3)(1.1) ?
The tangent of (4x)/(x+3)(1.1) is y=(13.2)/((a_{0)+3)^2}x+(4.4a_{0}^2)/((a_{0)+3)^2}