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

解

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

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

解答ステップ

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

x, y, z

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 t} (cos (\frac{z}{t}))

連鎖法則を適用:

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

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

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

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

簡素化

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

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