(\partial}{\partial x}(\frac{{Y}(x))/x)

解

\frac{\partial}{\partial x} (\frac{Y ( x )}{x})

\frac{x \frac{\partial}{\partial x} ( Y ( x ) ) - Y ( x )}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{Y ( x )}{x})

商の法則を適用:

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

= \frac{\frac{\partial}{\partial x} ( Y ( x ) ) x - \frac{\partial}{\partial x} ( x ) Y ( x )}{x ^{2}}

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

= \frac{\frac{\partial}{\partial x} ( Y ( x ) ) x - 1 \cdot Y ( x )}{x ^{2}}

簡素化

= \frac{x \frac{\partial}{\partial x} ( Y ( x ) ) - Y ( x )}{x ^{2}}