(\partial)/(\partial t)((8.31t)/(V(t)))

解

\frac{\partial}{\partial t} (\frac{8.31 t}{V ( t )})

\frac{8.31 ( V ( t ) - t \frac{\partial}{\partial t} ( V ( t ) ) )}{V ( t ) ^{2}}

解答ステップ

\frac{\partial}{\partial t} (\frac{8.31 t}{V ( t )})

定数を除去:

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

= 8.31 \frac{\partial}{\partial t} (\frac{t}{V ( t )})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 8.31 \cdot \frac{\frac{\partial}{\partial t} ( t ) V ( t ) - \frac{\partial}{\partial t} ( V ( t ) ) t}{V ( t ) ^{2}}

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

= 8.31 \cdot \frac{1 \cdot V ( t ) - \frac{\partial}{\partial t} ( V ( t ) ) t}{V ( t ) ^{2}}

簡素化

8.31 \cdot \frac{1 \cdot V ( t ) - \frac{\partial}{\partial t} ( V ( t ) ) t}{V ( t ) ^{2}} : \frac{8.31 ( V ( t ) - t \frac{\partial}{\partial t} ( V ( t ) ) )}{V ( t ) ^{2}}

= \frac{8.31 ( V ( t ) - t \frac{\partial}{\partial t} ( V ( t ) ) )}{V ( t ) ^{2}}