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

解答

\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}}

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

(\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}}

化简

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}}

x \to 2 lim (\frac{2 x - 6}{x - 1})

x \to 9 - lim (\frac{5 x}{x - 9})

\frac{d}{d x} (- 4 x^{4} + 8 x^{3})

in v erse l a pl a ce \frac{( 3 s + 1 )}{s ( s + 2 )}

y^{^{'}} - \frac{6}{x} y = \frac{( y ^{5} )}{x ^{18}}, y (1) = 1