derivative of arcsin(4x^4)

解

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

\frac{16 x ^{3}}{1 - 16 x ^{8}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

= \frac{1}{1 - ( 4 x ^{4} ) ^{2}} \cdot 16 x^{3}

簡素化

\frac{1}{1 - ( 4 x ^{4} ) ^{2}} \cdot 16 x^{3} : \frac{16 x ^{3}}{1 - 16 x ^{8}}

= \frac{16 x ^{3}}{1 - 16 x ^{8}}