(\partial)/(\partial y)(ln(x+sqrt(y)))

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

= \frac{1}{x + y} \cdot \frac{1}{2 y}

簡素化

\frac{1}{x + y} \cdot \frac{1}{2 y} : \frac{1}{2 y ( x + y )}

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