What is the tangent of (x^2)/(x+2) ?

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

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tangent of (x^2)/(x+2)

tangent of

\frac{x ^{2}}{x + 2}

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

Find the slope of

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

Compute the slope of

y = \frac{x ^{2}}{x + 2}

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

Find the line with slope m=

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

and passing through

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

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

\frac{d}{d x} (A x^{2} + B x)

\int cos (5 x) sin (6 x) d x

\int x x + 3 d x

\frac{d y}{d x} = \frac{( x + 3 y )}{y - 3 x}

x \to 3 lim (\frac{x ^{3} - 6 x ^{2} + 9}{x ^{2} - 9})

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