(\partial)/(\partial y)(e^{xy^2+z^2})

解

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

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

解答ステップ

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

x, z

を定数として扱う

連鎖法則を適用:

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

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

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

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