(\partial)/(\partial y)(ln(x+y^2))

解

\frac{\partial}{\partial y} (ln (x + y^{2}))

\frac{2 y}{x + y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (ln (x + y^{2}))

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{x + y ^{2}} \cdot 2 y : \frac{2 y}{x + y ^{2}}

= \frac{2 y}{x + y ^{2}}