(\partial)/(\partial y)(e^{xy}tan(y))

解

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

e^{x y} x tan (y) + sec^{2} (y) e^{x y}

解答ステップ

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

x

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y}, g = tan (y)

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

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

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

= e^{x y} x tan (y) + sec^{2} (y) e^{x y}