derivative y=(tsin(t))^2+tsin(t)

解

導関数

y = (t \cdot sin (t))^{2} + t \cdot sin (t)

2 t sin^{2} (t) + sin (2 t) t^{2} + sin (t) + t cos (t)

解答ステップ

\frac{d}{d t} ((t sin (t))^{2} + t sin (t))

簡素化

(t sin (t))^{2} + t sin (t) : t^{2} sin^{2} (t) + t sin (t)

= \frac{d}{d t} (t^{2} sin^{2} (t) + t sin (t))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{2} sin^{2} (t)) + \frac{d}{d t} (t sin (t))

\frac{d}{d t} (t^{2} sin^{2} (t)) = 2 t sin^{2} (t) + sin (2 t) t^{2}

\frac{d}{d t} (t sin (t)) = sin (t) + t cos (t)

= 2 t sin^{2} (t) + sin (2 t) t^{2} + sin (t) + t cos (t)