(\partial)/(\partial x)(log_{e}(x+y))

解

\frac{\partial}{\partial x} (lo g_{e} (x + y))

\frac{1}{x + y}

解答ステップ

\frac{\partial}{\partial x} (lo g_{e} (x + y))

簡素化

lo g_{e} (x + y) : ln (x + y)

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= \frac{1}{x + y} \cdot 1

簡素化

= \frac{1}{x + y}