(\partial)/(\partial y)((x)((1+e^x)ln(y)))

解

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

\frac{x ( 1 + e ^{x} )}{y}

解答ステップ

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

x

を定数として扱う

定数を除去:

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

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

共通の導関数を適用:

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

= x (1 + e^{x}) \frac{1}{y}

簡素化

x (1 + e^{x}) \frac{1}{y} : \frac{x ( 1 + e ^{x} )}{y}

= \frac{x ( 1 + e ^{x} )}{y}