(\partial)/(\partial x)((7x+y)(e^x))

解

\frac{\partial}{\partial x} ((7 x + y) (e^{x}))

7 e^{x} + e^{x} (7 x + y)

解答ステップ

\frac{\partial}{\partial x} ((7 x + y) (e^{x}))

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 = 7 x + y, g = e^{x}

= \frac{\partial}{\partial x} (7 x + y) e^{x} + \frac{\partial}{\partial x} (e^{x}) (7 x + y)

\frac{\partial}{\partial x} (7 x + y) = 7

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

= 7 e^{x} + e^{x} (7 x + y)