(\partial)/(\partial x)(3e^{5x})

解

\frac{\partial}{\partial x} (3 e^{5 x})

15 e^{5 x}

解答ステップ

\frac{\partial}{\partial x} (3 e^{5 x})

定数を除去:

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

= 3 \frac{\partial}{\partial x} (e^{5 x})

連鎖法則を適用:

e^{5 x} \frac{\partial}{\partial x} (5 x)

= e^{5 x} \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= 3 e^{5 x} \cdot 5

簡素化

= 15 e^{5 x}