(\partial)/(\partial x)(e^xsin(x+y))

解

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

e^{x} sin (x + y) + cos (x + y) e^{x}

解答ステップ

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

y

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}, g = sin (x + y)

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

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

\frac{\partial}{\partial x} (sin (x + y)) = cos (x + y)

= e^{x} sin (x + y) + cos (x + y) e^{x}