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人気のある微分積分 >

(arctan(x^2))^'

解

(arctan (x^{2}))^{^{'}}

解

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

解答ステップ

(arctan (x^{2}))^{'}

連鎖法則を適用:

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

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

(x^{2})^{'} = 2 x

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

簡素化

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

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

グラフ

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