(\partial)/(\partial y)(sqrt(1+x^2+y^2))

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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