(\partial)/(\partial z)(x^2ycos(z/t))

解

\frac{\partial}{\partial z} (x^{2} y cos (\frac{z}{t}))

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

解答ステップ

\frac{\partial}{\partial z} (x^{2} y cos (\frac{z}{t}))

x, y, t

を定数として扱う

定数を除去:

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

= x^{2} y \frac{\partial}{\partial z} (cos (\frac{z}{t}))

連鎖法則を適用:

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

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

\frac{\partial}{\partial z} (\frac{z}{t}) = \frac{1}{t}

= x^{2} y (- sin (\frac{z}{t}) \frac{1}{t})

簡素化

x^{2} y (- sin (\frac{z}{t}) \frac{1}{t}) : - \frac{x ^{2} y sin ( \frac{z}{t} )}{t}

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