derivative 12arctan(sqrt(s))

解

導関数

12 arctan (s)

\frac{6}{s ( s + 1 )}

解答ステップ

\frac{d}{d s} (12 arctan (s))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d s} (arctan (s))

連鎖法則を適用:

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

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

\frac{d}{d s} (s) = \frac{1}{2 s}

= 12 \cdot \frac{1}{( s ) ^{2} + 1} \cdot \frac{1}{2 s}

簡素化

12 \cdot \frac{1}{( s ) ^{2} + 1} \cdot \frac{1}{2 s} : \frac{6}{s ( s + 1 )}

= \frac{6}{s ( s + 1 )}