What is the tangent of (x^2)/(x^2+7) ?

The tangent of (x^2)/(x^2+7) is y=(14a_{0})/((a_{0)^2+7)^2}x+(a_{0}^4-7a_{0}^2)/((a_{0)^2+7)^2}

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tangent of (x^2)/(x^2+7)

tangent of

\frac{x ^{2}}{x ^{2} + 7}

y = \frac{14 a _{0}}{( a _{0}^{2} + 7 ) ^{2}} x + \frac{a _{0}^{4} - 7 a _{0}^{2}}{( a _{0}^{2} + 7 ) ^{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} + 7})

Find the slope of

y = \frac{x ^{2}}{x ^{2} + 7} : \frac{d y}{d x} = \frac{14 x}{( x ^{2} + 7 ) ^{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{14 a _{0}}{( a _{0}^{2} + 7 ) ^{2}}

Find the line with slope m=

\frac{14 a _{0}}{( a _{0}^{2} + 7 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}^{2}}{a _{0}^{2} + 7}) : y = \frac{14 a _{0}}{( a _{0}^{2} + 7 ) ^{2}} x + \frac{a _{0}^{4} - 7 a _{0}^{2}}{( a _{0}^{2} + 7 ) ^{2}}

y = \frac{14 a _{0}}{( a _{0}^{2} + 7 ) ^{2}} x + \frac{a _{0}^{4} - 7 a _{0}^{2}}{( a _{0}^{2} + 7 ) ^{2}}

What is the tangent of (x^2)/(x^2+7) ?
The tangent of (x^2)/(x^2+7) is y=(14a_{0})/((a_{0)^2+7)^2}x+(a_{0}^4-7a_{0}^2)/((a_{0)^2+7)^2}