derivative of x^3*sin^2(5x)

解

\frac{d}{d x} (x^{3} \cdot sin^{2} (5 x))

3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}

解答ステップ

\frac{d}{d x} (x^{3} sin^{2} (5 x))

積の法則を適用:

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

f = x^{3}, g = sin^{2} (5 x)

= \frac{d}{d x} (x^{3}) sin^{2} (5 x) + \frac{d}{d x} (sin^{2} (5 x)) x^{3}

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

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= 3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}