(\partial)/(\partial y)(e^{x^2-y^2+4y})

解

\frac{\partial}{\partial y} (e^{x^{2} - y^{2} + 4 y})

e^{x^{2} - y^{2} + 4 y} (- 2 y + 4)

解答ステップ

\frac{\partial}{\partial y} (e^{x^{2} - y^{2} + 4 y})

x

を定数として扱う

連鎖法則を適用:

e^{x^{2} - y^{2} + 4 y} \frac{\partial}{\partial y} (x^{2} - y^{2} + 4 y)

= e^{x^{2} - y^{2} + 4 y} \frac{\partial}{\partial y} (x^{2} - y^{2} + 4 y)

\frac{\partial}{\partial y} (x^{2} - y^{2} + 4 y) = - 2 y + 4

= e^{x^{2} - y^{2} + 4 y} (- 2 y + 4)