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人気のある微分積分 >

derivative f(x)=sqrt(2x^2+1)

解

導関数

f (x) = 2 x^{2} + 1

解

\frac{2 x}{2 x ^{2} + 1}

解答ステップ

\frac{d}{d x} (2 x^{2} + 1)

連鎖法則を適用:

\frac{1}{2 2 x ^{2} + 1} \frac{d}{d x} (2 x^{2} + 1)

= \frac{1}{2 2 x ^{2} + 1} \frac{d}{d x} (2 x^{2} + 1)

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{1}{2 2 x ^{2} + 1} \cdot 4 x

簡素化

\frac{1}{2 2 x ^{2} + 1} \cdot 4 x : \frac{2 x}{2 x ^{2} + 1}

= \frac{2 x}{2 x ^{2} + 1}

グラフ

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