(\partial)/(\partial y)(xe^{2y}sin(7z))

解

\frac{\partial}{\partial y} (x e^{2 y} sin (7 z))

x sin (7 z) e^{2 y} \cdot 2

解答ステップ

\frac{\partial}{\partial y} (x e^{2 y} sin (7 z))

x, z

を定数として扱う

定数を除去:

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

= x sin (7 z) \frac{\partial}{\partial y} (e^{2 y})

連鎖法則を適用:

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

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

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

= x sin (7 z) e^{2 y} \cdot 2