derivative of 12arccot(ax^2)

解

\frac{d}{d x} (12 arccot (a x^{2}))

- \frac{24 a x}{a ^{2} x ^{4} + 1}

解答ステップ

\frac{d}{d x} (12 arccot (a x^{2}))

定数を除去:

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

= 12 \frac{d}{d x} (arccot (a x^{2}))

連鎖法則を適用:

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

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

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

= 12 (- \frac{1}{( a x ^{2} ) ^{2} + 1} \cdot 2 a x)

簡素化

12 (- \frac{1}{( a x ^{2} ) ^{2} + 1} \cdot 2 a x) : - \frac{24 a x}{a ^{2} x ^{4} + 1}

= - \frac{24 a x}{a ^{2} x ^{4} + 1}