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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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