(\partial)/(\partial x)(sin(xye^{x^2}))

解

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

cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})