derivative of arctan(sqrt(3x))

解

\frac{d}{d x} (arctan (3 x))

\frac{3}{2 x ( 3 x + 1 )}

解答ステップ

\frac{d}{d x} (arctan (3 x))

簡素化

arctan (3 x) : arctan (3 x)

= \frac{d}{d x} (arctan (3 x))

連鎖法則を適用:

\frac{1}{( 3 x ) ^{2} + 1} \frac{d}{d x} (3 x)

= \frac{1}{( 3 x ) ^{2} + 1} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= \frac{1}{( 3 x ) ^{2} + 1} \cdot \frac{3}{2 x}

簡素化

\frac{1}{( 3 x ) ^{2} + 1} \cdot \frac{3}{2 x} : \frac{3}{2 x ( 3 x + 1 )}

= \frac{3}{2 x ( 3 x + 1 )}