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

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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