derivative of 6arcsin(x^4)

解

\frac{d}{d x} (6 arcsin (x^{4}))

\frac{24 x ^{3}}{1 - x ^{8}}

解答ステップ

\frac{d}{d x} (6 arcsin (x^{4}))

定数を除去:

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

= 6 \frac{d}{d x} (arcsin (x^{4}))

連鎖法則を適用:

\frac{1}{1 - ( x ^{4} ) ^{2}} \frac{d}{d x} (x^{4})

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

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

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

簡素化

6 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{24 x ^{3}}{1 - x ^{8}}

= \frac{24 x ^{3}}{1 - x ^{8}}