(\partial)/(\partial y)(x^2e^{5xy})

解

\frac{\partial}{\partial y} (x^{2} e^{5 x y})

5 e^{5 x y} x^{3}

解答ステップ

\frac{\partial}{\partial y} (x^{2} e^{5 x y})

x

を定数として扱う

定数を除去:

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

= x^{2} \frac{\partial}{\partial y} (e^{5 x y})

連鎖法則を適用:

e^{5 x y} \frac{\partial}{\partial y} (5 x y)

= e^{5 x y} \frac{\partial}{\partial y} (5 x y)

\frac{\partial}{\partial y} (5 x y) = 5 x

= x^{2} e^{5 x y} \cdot 5 x

簡素化

x^{2} e^{5 x y} \cdot 5 x : 5 e^{5 x y} x^{3}

= 5 e^{5 x y} x^{3}