(\partial)/(\partial x)((x+2)/(y-2)+1/x)

解

\frac{\partial}{\partial x} (\frac{x + 2}{y - 2} + \frac{1}{x})

\frac{1}{y - 2} - \frac{1}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{x + 2}{y - 2} + \frac{1}{x})

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{1}{y - 2} - \frac{1}{x ^{2}}