tangent (x^3-16x)^8

Lösung

tangente von

(x^{3} - 16 x)^{8}

y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

Schritte zur Lösung

Berechne den Graphen der Tangente für den allgemeinen Punkt

x = a_{0}

Finde den Tangentenpunkt:

(a_{0}, (a_{0}^{3} - 16 a_{0})^{8})

Finde die Steigung von

y = (x^{3} - 16 x)^{8} : \frac{d y}{d x} = 8 (x^{3} - 16 x)^{7} (3 x^{2} - 16)

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}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16)

Finde den Graphen mit Steigung m=

8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16)

, der durch den Punkt

(a_{0}, (a_{0}^{3} - 16 a_{0})^{8})

verläuft:

y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

y = 8 (a_{0}^{3} - 16 a_{0})^{7} (3 a_{0}^{2} - 16) x - 23 a_{0}^{24} + 2688 a_{0}^{22} - 136192 a_{0}^{20} + 3899392 a_{0}^{18} - 68812800 a_{0}^{16} + 763363328 a_{0}^{14} - 5167382528 a_{0}^{12} + 19327352832 a_{0}^{10} + 1 6^{8} a_{0}^{8} - 34359738368 a_{0}^{8}

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

\frac{d}{d x} (sec (0))

\int (4 - x^{2})^{\frac{1}{2}} d x

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