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

解

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

- \frac{11 t}{( x - 2 t ) ^{2}}

解答ステップ

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

t

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

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

\frac{\partial}{\partial x} (x - 2 t) = 1

= \frac{4 ( x - 2 t ) - 1 \cdot ( 4 x + 3 t )}{( x - 2 t ) ^{2}}

簡素化

\frac{4 ( x - 2 t ) - 1 \cdot ( 4 x + 3 t )}{( x - 2 t ) ^{2}} : - \frac{11 t}{( x - 2 t ) ^{2}}

= - \frac{11 t}{( x - 2 t ) ^{2}}