derivative of 4x^2cos(3x)

解

\frac{d}{d x} (4 x^{2} cos (3 x))

4 (2 x cos (3 x) - 3 x^{2} sin (3 x))

解答ステップ

\frac{d}{d x} (4 x^{2} cos (3 x))

定数を除去:

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

= 4 \frac{d}{d x} (x^{2} cos (3 x))

積の法則を適用:

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

f = x^{2}, g = cos (3 x)

= 4 (\frac{d}{d x} (x^{2}) cos (3 x) + \frac{d}{d x} (cos (3 x)) x^{2})

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 4 (2 x cos (3 x) + (- sin (3 x) \cdot 3) x^{2})

簡素化

= 4 (2 x cos (3 x) - 3 x^{2} sin (3 x))