derivative of arctan(sqrt(2x^3))

解

\frac{d}{d x} (arctan (2 x^{3}))

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

解答ステップ

\frac{d}{d x} (arctan (2 x^{3}))

簡素化

arctan (2 x^{3}) : arctan (2 x^{3})

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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