(\partial)/(\partial x)(y-ln(sqrt(xy)))

解

\frac{\partial}{\partial x} (y - ln (x y))

- \frac{1}{2 x}

解答ステップ

\frac{\partial}{\partial x} (y - ln (x y))

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} (y) - \frac{\partial}{\partial x} (ln (x y))

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{1}{2 x}

簡素化

= - \frac{1}{2 x}