(\partial)/(\partial y)(e^{x^2+y^2-2})

解

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

e^{x^{2} + y^{2} - 2} \cdot 2 y

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

= e^{x^{2} + y^{2} - 2} \cdot 2 y