(\partial)/(\partial x)((c^2-x^2)/(2x))

解

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

\frac{- x ^{2} - c ^{2}}{2 x ^{2}}

解答ステップ

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

定数を除去:

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

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

商の法則を適用:

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

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

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

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

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

簡素化

\frac{1}{2} \cdot \frac{( - 2 x ) x - 1 \cdot ( c ^{2} - x ^{2} )}{x ^{2}} : \frac{- x ^{2} - c ^{2}}{2 x ^{2}}

= \frac{- x ^{2} - c ^{2}}{2 x ^{2}}