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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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