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

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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