(\partial)/(\partial y)(8xe^{x^2+y^2})

解

\frac{\partial}{\partial y} (8 x e^{x^{2} + y^{2}})

16 e^{x^{2} + y^{2}} x y

解答ステップ

\frac{\partial}{\partial y} (8 x e^{x^{2} + y^{2}})

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 x \frac{\partial}{\partial y} (e^{x^{2} + y^{2}})

連鎖法則を適用:

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

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

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

= 8 x e^{x^{2} + y^{2}} \cdot 2 y

簡素化

= 16 e^{x^{2} + y^{2}} x y