(\partial)/(\partial y)(sqrt(y^2-9))

解

\frac{\partial}{\partial y} (y^{2} - 9)

\frac{y}{y ^{2} - 9}

解答ステップ

\frac{\partial}{\partial y} (y^{2} - 9)

連鎖法則を適用:

\frac{1}{2 y ^{2} - 9} \frac{\partial}{\partial y} (y^{2} - 9)

= \frac{1}{2 y ^{2} - 9} \frac{\partial}{\partial y} (y^{2} - 9)

\frac{\partial}{\partial y} (y^{2} - 9) = 2 y

= \frac{1}{2 y ^{2} - 9} \cdot 2 y

簡素化

\frac{1}{2 y ^{2} - 9} \cdot 2 y : \frac{y}{y ^{2} - 9}

= \frac{y}{y ^{2} - 9}