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人気のある微分積分 >

tangent y=(x^3-4x)^{10}

解

タンジェント

y = (x^{3} - 4 x)^{10}

解

y = 10 (a_{0}^{3} - 4 a_{0})^{9} (3 a_{0}^{2} - 4) x - 29 a_{0}^{30} + 1080 a_{0}^{28} - 18000 a_{0}^{26} + 176640 a_{0}^{24} - 1128960 a_{0}^{22} + 4902912 a_{0}^{20} - 14622720 a_{0}^{18} + 29491200 a_{0}^{16} - 38338560 a_{0}^{14} + 28835840 a_{0}^{12} - 9437184 a_{0}^{10}

解答ステップ

一般的なポイントへの接線を計算する

x = a_{0}

接点を見つける:

(a_{0}, (a_{0}^{3} - 4 a_{0})^{10})

以下の傾斜を見つける:

y = (x^{3} - 4 x)^{10} : \frac{d y}{d x} = 10 (x^{3} - 4 x)^{9} (3 x^{2} - 4)

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 = 10 (a_{0}^{3} - 4 a_{0})^{9} (3 a_{0}^{2} - 4)

傾斜m=

10 (a_{0}^{3} - 4 a_{0})^{9} (3 a_{0}^{2} - 4)

で通過する線を見つける

(a_{0}, (a_{0}^{3} - 4 a_{0})^{10}) : y = 10 (a_{0}^{3} - 4 a_{0})^{9} (3 a_{0}^{2} - 4) x - 29 a_{0}^{30} + 1080 a_{0}^{28} - 18000 a_{0}^{26} + 176640 a_{0}^{24} - 1128960 a_{0}^{22} + 4902912 a_{0}^{20} - 14622720 a_{0}^{18} + 29491200 a_{0}^{16} - 38338560 a_{0}^{14} + 28835840 a_{0}^{12} - 9437184 a_{0}^{10}

y = 10 (a_{0}^{3} - 4 a_{0})^{9} (3 a_{0}^{2} - 4) x - 29 a_{0}^{30} + 1080 a_{0}^{28} - 18000 a_{0}^{26} + 176640 a_{0}^{24} - 1128960 a_{0}^{22} + 4902912 a_{0}^{20} - 14622720 a_{0}^{18} + 29491200 a_{0}^{16} - 38338560 a_{0}^{14} + 28835840 a_{0}^{12} - 9437184 a_{0}^{10}

グラフ

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