(\partial)/(\partial x)(arcsin(-2x^4))

解

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

- \frac{8 x ^{3}}{1 - 4 x ^{8}}

解答ステップ

\frac{\partial}{\partial x} (arcsin (- 2 x^{4}))

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (- 2 x^{4}) = - 8 x^{3}

= \frac{1}{1 - ( - 2 x ^{4} ) ^{2}} (- 8 x^{3})

簡素化

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

= - \frac{8 x ^{3}}{1 - 4 x ^{8}}