(\partial)/(\partial x)((4x-3t)/(s+2x))

解

\frac{\partial}{\partial x} (\frac{4 x - 3 t}{s + 2 x})

\frac{4 s + 6 t}{( s + 2 x ) ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{4 x - 3 t}{s + 2 x})

t, s

を定数として扱う

商の法則を適用:

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

= \frac{\frac{\partial}{\partial x} ( 4 x - 3 t ) ( s + 2 x ) - \frac{\partial}{\partial x} ( s + 2 x ) ( 4 x - 3 t )}{( s + 2 x ) ^{2}}

\frac{\partial}{\partial x} (4 x - 3 t) = 4

\frac{\partial}{\partial x} (s + 2 x) = 2

= \frac{4 ( s + 2 x ) - 2 ( 4 x - 3 t )}{( s + 2 x ) ^{2}}

拡張

4 (s + 2 x) - 2 (4 x - 3 t) : 4 s + 6 t

= \frac{4 s + 6 t}{( s + 2 x ) ^{2}}