derivative e^{arctan(3x^2)}

解

導関数

e^{a r c t a n (3 x^{2})}

\frac{6 e ^{a r c t a n (3 x^{2})} x}{9 x ^{4} + 1}

解答ステップ

\frac{d}{d x} (e^{a r c t a n (3 x^{2})})

連鎖法則を適用:

e^{a r c t a n (3 x^{2})} \frac{d}{d x} (arctan (3 x^{2}))

= e^{a r c t a n (3 x^{2})} \frac{d}{d x} (arctan (3 x^{2}))

\frac{d}{d x} (arctan (3 x^{2})) = \frac{6 x}{9 x ^{4} + 1}

= e^{a r c t a n (3 x^{2})} \frac{6 x}{9 x ^{4} + 1}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 e ^{a r c t a n (3 x^{2})} x}{9 x ^{4} + 1}