(\partial)/(\partial y)(3xz^3e^{y^2})

解

\frac{\partial}{\partial y} (3 x z^{3} e^{y^{2}})

6 e^{y^{2}} x z^{3} y

解答ステップ

\frac{\partial}{\partial y} (3 x z^{3} e^{y^{2}})

x, z

を定数として扱う

定数を除去:

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

= 3 x z^{3} \frac{\partial}{\partial y} (e^{y^{2}})

連鎖法則を適用:

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

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

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

= 3 x z^{3} e^{y^{2}} \cdot 2 y

簡素化

= 6 e^{y^{2}} x z^{3} y