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人気のある微分積分 >

derivative of arctan(x+2)

解

\frac{d}{d x} (arctan (x + 2))

解

\frac{1}{x ^{2} + 4 x + 5}

解答ステップ

\frac{d}{d x} (arctan (x + 2))

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{( x + 2 ) ^{2} + 1} \cdot 1 : \frac{1}{x ^{2} + 4 x + 5}

= \frac{1}{x ^{2} + 4 x + 5}

グラフ

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