derivative of arcsin(3x^4)

解

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

\frac{12 x ^{3}}{1 - 9 x ^{8}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

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

簡素化

\frac{1}{1 - ( 3 x ^{4} ) ^{2}} \cdot 12 x^{3} : \frac{12 x ^{3}}{1 - 9 x ^{8}}

= \frac{12 x ^{3}}{1 - 9 x ^{8}}