derivative of sqrt(11arctan(x))

解

\frac{d}{d x} (11 arctan (x))

\frac{11}{2 arctan ( x ) ( x ^{2} + 1 )}

解答ステップ

\frac{d}{d x} (11 arctan (x))

連鎖法則を適用:

\frac{1}{2 11 arctan ( x )} \frac{d}{d x} (11 arctan (x))

= \frac{1}{2 11 arctan ( x )} \frac{d}{d x} (11 arctan (x))

\frac{d}{d x} (11 arctan (x)) = \frac{11}{x ^{2} + 1}

= \frac{1}{2 11 arctan ( x )} \cdot \frac{11}{x ^{2} + 1}

簡素化

\frac{1}{2 11 arctan ( x )} \cdot \frac{11}{x ^{2} + 1} : \frac{11}{2 arctan ( x ) ( x ^{2} + 1 )}

= \frac{11}{2 arctan ( x ) ( x ^{2} + 1 )}