(\partial)/(\partial y)(x-z-arctan(yz))

解

\frac{\partial}{\partial y} (x - z - arctan (yz))

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

解答ステップ

\frac{\partial}{\partial y} (x - z - arctan (yz))

x, z

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (x) - \frac{\partial}{\partial y} (z) - \frac{\partial}{\partial y} (arctan (yz))

\frac{\partial}{\partial y} (x) = 0

\frac{\partial}{\partial y} (z) = 0

\frac{\partial}{\partial y} (arctan (yz)) = \frac{z}{z ^{2} y ^{2} + 1}

= 0 - 0 - \frac{z}{z ^{2} y ^{2} + 1}

簡素化

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