(\partial)/(\partial z)(xcos(y/z))

解

\frac{\partial}{\partial z} (x cos (\frac{y}{z}))

\frac{x y sin ( \frac{y}{z} )}{z ^{2}}

解答ステップ

\frac{\partial}{\partial z} (x cos (\frac{y}{z}))

x, y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial z} (cos (\frac{y}{z}))

連鎖法則を適用:

- sin (\frac{y}{z}) \frac{\partial}{\partial z} (\frac{y}{z})

= - sin (\frac{y}{z}) \frac{\partial}{\partial z} (\frac{y}{z})

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

= x (- sin (\frac{y}{z}) (- \frac{y}{z ^{2}}))

簡素化

x (- sin (\frac{y}{z}) (- \frac{y}{z ^{2}})) : \frac{x y sin ( \frac{y}{z} )}{z ^{2}}

= \frac{x y sin ( \frac{y}{z} )}{z ^{2}}