derivative of x^2cos^2(x)

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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

簡素化

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