(\partial)/(\partial x)(4sin(4x)e^{3x})

解

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

4 (cos (4 x) \cdot 4 e^{3 x} + e^{3 x} \cdot 3 sin (4 x))

解答ステップ

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

定数を除去:

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

= 4 \frac{\partial}{\partial x} (sin (4 x) e^{3 x})

積の法則を適用:

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

f = sin (4 x), g = e^{3 x}

= 4 (\frac{\partial}{\partial x} (sin (4 x)) e^{3 x} + \frac{\partial}{\partial x} (e^{3 x}) sin (4 x))

\frac{\partial}{\partial x} (sin (4 x)) = cos (4 x) \cdot 4

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

= 4 (cos (4 x) \cdot 4 e^{3 x} + e^{3 x} \cdot 3 sin (4 x))