What is the tangent of y=(5x)/(x+2)(3.3) ?

The tangent of y=(5x)/(x+2)(3.3) is y=(33)/((a_{0)+2)^2}x+(16.5a_{0}^2)/((a_{0)+2)^2}

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tangent of y=(5x)/(x+2)(3.3)

tangent of

y = \frac{5 x}{x + 2} (3.3)

y = \frac{33}{( a _{0} + 2 ) ^{2}} x + \frac{16.5 a _{0}^{2}}{( a _{0} + 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{16.5 a _{0}}{a _{0} + 2})

Find the slope of

y = \frac{5 x}{x + 2} 3.3 : \frac{d y}{d x} = \frac{33}{( x + 2 ) ^{2}}

Compute the slope of

y = \frac{5 x}{x + 2} 3.3

x = a_{0} : m = \frac{33}{( a _{0} + 2 ) ^{2}}

Find the line with slope m=

\frac{33}{( a _{0} + 2 ) ^{2}}

and passing through

(a_{0}, \frac{16.5 a _{0}}{a _{0} + 2}) : y = \frac{33}{( a _{0} + 2 ) ^{2}} x + \frac{16.5 a _{0}^{2}}{( a _{0} + 2 ) ^{2}}

y = \frac{33}{( a _{0} + 2 ) ^{2}} x + \frac{16.5 a _{0}^{2}}{( a _{0} + 2 ) ^{2}}

\frac{d y}{d x} = - \frac{x + 6}{7 y ^{2}}

x \to - \frac{π}{3} lim (sec (x))

\frac{\partial}{\partial x} (- arctan (\frac{y}{x}))

4 x^{2} + 5 y \frac{d y}{d x} = 0

x^{^{''}} + x^{^{'}} - 2 x = e^{t}

What is the tangent of y=(5x)/(x+2)(3.3) ?
The tangent of y=(5x)/(x+2)(3.3) is y=(33)/((a_{0)+2)^2}x+(16.5a_{0}^2)/((a_{0)+2)^2}