(\partial)/(\partial y)(sqrt(1-y^2))

解

\frac{\partial}{\partial y} (1 - y^{2})

- \frac{y}{1 - y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (1 - y^{2})

連鎖法則を適用:

\frac{1}{2 1 - y ^{2}} \frac{\partial}{\partial y} (1 - y^{2})

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

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

= \frac{1}{2 1 - y ^{2}} (- 2 y)

簡素化

\frac{1}{2 1 - y ^{2}} (- 2 y) : - \frac{y}{1 - y ^{2}}

= - \frac{y}{1 - y ^{2}}