(\partial)/(\partial x)(1/y+xln(y))

解

\frac{\partial}{\partial x} (\frac{1}{y} + x ln (y))

ln (y)

解答ステップ

\frac{\partial}{\partial x} (\frac{1}{y} + x ln (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} (\frac{1}{y}) + \frac{\partial}{\partial x} (x ln (y))

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

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

= 0 + ln (y)

簡素化

= ln (y)