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

解

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

\frac{4 x}{x ^{2} + y ^{2}}

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{2}) = 4 x (x^{2} + y^{2})

= \frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 4 x (x^{2} + y^{2})

簡素化

\frac{1}{( x ^{2} + y ^{2} ) ^{2}} \cdot 4 x (x^{2} + y^{2}) : \frac{4 x}{x ^{2} + y ^{2}}

= \frac{4 x}{x ^{2} + y ^{2}}