(\partial}{\partial x}(\frac{(p(q,x)-cq))/x)

解

\frac{\partial}{\partial x} (\frac{( p ( q , x ) - c q )}{x})

\frac{( \frac{\partial}{\partial x} ( p ( q , x ) ) - 0 ) x - 1 \cdot ( p ( q , x ) - c q )}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{( p ( q , x ) - c q )}{x})

c, q

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} ( p ( q , x ) - c q ) x - \frac{\partial}{\partial x} ( x ) ( p ( q , x ) - c q )}{x ^{2}}

\frac{\partial}{\partial x} (p (q, x) - c q) = \frac{\partial}{\partial x} (p (q, x)) - 0

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

= \frac{( \frac{\partial}{\partial x} ( p ( q , x ) ) - 0 ) x - 1 \cdot ( p ( q , x ) - c q )}{x ^{2}}