derivative 4arcsin(x^3)

解

導関数

4 arcsin (x^{3})

\frac{12 x ^{2}}{1 - x ^{6}}

解答ステップ

\frac{d}{d x} (4 arcsin (x^{3}))

定数を除去:

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

= 4 \frac{d}{d x} (arcsin (x^{3}))

連鎖法則を適用:

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

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

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

= 4 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2}

簡素化

4 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{12 x ^{2}}{1 - x ^{6}}

= \frac{12 x ^{2}}{1 - x ^{6}}