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人気のある微分積分 >

derivative f(x)=(9x^6+2x^3)^4

解

導関数

f (x) = (9 x^{6} + 2 x^{3})^{4}

解

4 (9 x^{6} + 2 x^{3})^{3} (54 x^{5} + 6 x^{2})

解答ステップ

\frac{d}{d x} ((9 x^{6} + 2 x^{3})^{4})

連鎖法則を適用:

4 (9 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (9 x^{6} + 2 x^{3})

= 4 (9 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (9 x^{6} + 2 x^{3})

\frac{d}{d x} (9 x^{6} + 2 x^{3}) = 54 x^{5} + 6 x^{2}

= 4 (9 x^{6} + 2 x^{3})^{3} (54 x^{5} + 6 x^{2})

グラフ

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