(\partial)/(\partial x)(7xe^{x^2}+y^2)

解

\frac{\partial}{\partial x} (7 x e^{x^{2}} + y^{2})

7 (2 e^{x^{2}} x^{2} + e^{x^{2}})

解答ステップ

\frac{\partial}{\partial x} (7 x e^{x^{2}} + y^{2})

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (7 x e^{x^{2}}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (7 x e^{x^{2}}) = 7 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

\frac{\partial}{\partial x} (y^{2}) = 0

= 7 (e^{x^{2}} + 2 e^{x^{2}} x^{2}) + 0

簡素化

= 7 (2 e^{x^{2}} x^{2} + e^{x^{2}})