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人気のある微分積分 >

derivative (5x^6+4x^3)^4

解

導関数

(5 x^{6} + 4 x^{3})^{4}

解

4 (5 x^{6} + 4 x^{3})^{3} (30 x^{5} + 12 x^{2})

解答ステップ

\frac{d}{d x} ((5 x^{6} + 4 x^{3})^{4})

連鎖法則を適用:

4 (5 x^{6} + 4 x^{3})^{3} \frac{d}{d x} (5 x^{6} + 4 x^{3})

= 4 (5 x^{6} + 4 x^{3})^{3} \frac{d}{d x} (5 x^{6} + 4 x^{3})

\frac{d}{d x} (5 x^{6} + 4 x^{3}) = 30 x^{5} + 12 x^{2}

= 4 (5 x^{6} + 4 x^{3})^{3} (30 x^{5} + 12 x^{2})

グラフ

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