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人気のある微分積分 >

derivative f(x)=x(x^2+6)

解

導関数

f (x) = x (x^{2} + 6)

解

3 x^{2} + 6

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + 6

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x^{2} + 6) + 2 xx

簡素化

1 \cdot (x^{2} + 6) + 2 xx : 3 x^{2} + 6

= 3 x^{2} + 6

グラフ

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