derivative of x^2sin(4x-3)

解

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

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

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = sin (4 x - 3)

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

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

\frac{d}{d x} (sin (4 x - 3)) = cos (4 x - 3) \cdot 4

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