derivative of 2x^2cos(4x)

解

\frac{d}{d x} (2 x^{2} cos (4 x))

2 (2 x cos (4 x) - 4 x^{2} sin (4 x))

解答ステップ

\frac{d}{d x} (2 x^{2} cos (4 x))

定数を除去:

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

= 2 \frac{d}{d x} (x^{2} cos (4 x))

積の法則を適用:

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

f = x^{2}, g = cos (4 x)

= 2 (\frac{d}{d x} (x^{2}) cos (4 x) + \frac{d}{d x} (cos (4 x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 (2 x cos (4 x) + (- sin (4 x) \cdot 4) x^{2})

簡素化

= 2 (2 x cos (4 x) - 4 x^{2} sin (4 x))