(\partial)/(\partial x)((2-sqrt(x))^6)

解

\frac{\partial}{\partial x} ((2 - x)^{6})

- \frac{3 ( - x + 2 ) ^{5}}{x}

解答ステップ

\frac{\partial}{\partial x} ((2 - x)^{6})

連鎖法則を適用:

6 (2 - x)^{5} \frac{\partial}{\partial x} (2 - x)

= 6 (2 - x)^{5} \frac{\partial}{\partial x} (2 - x)

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

= 6 (2 - x)^{5} (- \frac{1}{2 x})

簡素化

6 (2 - x)^{5} (- \frac{1}{2 x}) : - \frac{3 ( - x + 2 ) ^{5}}{x}

= - \frac{3 ( - x + 2 ) ^{5}}{x}