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人気のある微分積分 >

derivative of arctan(ax)

解

\frac{d}{d x} (arctan (a x))

解

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

解答ステップ

\frac{d}{d x} (arctan (a x))

連鎖法則を適用:

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

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

\frac{d}{d x} (a x) = a

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

簡素化

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

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

グラフ

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