What is the tangent of (x^2)/(x+3) ?

The tangent of (x^2)/(x+3) is y=(a_{0}^2+6a_{0})/((a_{0)+3)^2}x-(3a_{0}^2)/((a_{0)+3)^2}

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tangent of (x^2)/(x+3)

tangent of

\frac{x ^{2}}{x + 3}

y = \frac{a _{0}^{2} + 6 a _{0}}{( a _{0} + 3 ) ^{2}} x - \frac{3 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{a _{0}^{2}}{a _{0} + 3})

Find the slope of

y = \frac{x ^{2}}{x + 3} : \frac{d y}{d x} = \frac{x ^{2} + 6 x}{( x + 3 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{a _{0}^{2} + 6 a _{0}}{( a _{0} + 3 ) ^{2}}

Find the line with slope m=

\frac{a _{0}^{2} + 6 a _{0}}{( a _{0} + 3 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}^{2}}{a _{0} + 3}) : y = \frac{a _{0}^{2} + 6 a _{0}}{( a _{0} + 3 ) ^{2}} x - \frac{3 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

y = \frac{a _{0}^{2} + 6 a _{0}}{( a _{0} + 3 ) ^{2}} x - \frac{3 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

n = 0 \sum \infty 9 + 3 + 1

\frac{d}{d x} ((3 x^{2} - x + 5) (x^{2} + 3 x - 9))

\frac{\partial}{\partial y} (2 x^{4} y - 4)

\int sec (17 w) tan (17 w) d w

\frac{d}{d x} (ln (2 x - 1) + 2)

What is the tangent of (x^2)/(x+3) ?
The tangent of (x^2)/(x+3) is y=(a_{0}^2+6a_{0})/((a_{0)+3)^2}x-(3a_{0}^2)/((a_{0)+3)^2}