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人気のある微分積分 >

derivative f(x)=(8x^3+2x^2)^4

解

導関数

f (x) = (8 x^{3} + 2 x^{2})^{4}

解

4 (8 x^{3} + 2 x^{2})^{3} (24 x^{2} + 4 x)

解答ステップ

\frac{d}{d x} ((8 x^{3} + 2 x^{2})^{4})

連鎖法則を適用:

4 (8 x^{3} + 2 x^{2})^{3} \frac{d}{d x} (8 x^{3} + 2 x^{2})

= 4 (8 x^{3} + 2 x^{2})^{3} \frac{d}{d x} (8 x^{3} + 2 x^{2})

\frac{d}{d x} (8 x^{3} + 2 x^{2}) = 24 x^{2} + 4 x

= 4 (8 x^{3} + 2 x^{2})^{3} (24 x^{2} + 4 x)

グラフ

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