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Beliebt Rechnen >

tangent (x-6/x)^8

Lösung

tangente von

(x - \frac{6}{x})^{8}

Lösung

y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

Schritte zur Lösung

Berechne den Graphen der Tangente für den allgemeinen Punkt

x = a_{0}

Finde den Tangentenpunkt:

(a_{0}, (a_{0} - \frac{6}{a _{0}})^{8})

Finde die Steigung von

y = (x - \frac{6}{x})^{8} : \frac{d y}{d x} = 8 (x - \frac{6}{x})^{7} (1 + \frac{6}{x ^{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 = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}})

Finde den Graphen mit Steigung m=

8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}})

, der durch den Punkt

(a_{0}, (a_{0} - \frac{6}{a _{0}})^{8})

verläuft:

y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

y = 8 (a_{0} - \frac{6}{a _{0}})^{7} (1 + \frac{6}{a _{0}^{2}}) x - 7 a_{0}^{8} + 240 a_{0}^{6} - 3024 a_{0}^{4} + 12096 a_{0}^{2} - \frac{1306368}{a _{0}^{2}} + \frac{6531840}{a _{0}^{4}} - \frac{15676416}{a _{0}^{6}} + \frac{15116544}{a _{0}^{8}} + 90720

Graph

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y^{''}+5y^'+11y=33

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