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

Lösung

ableitung von

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)

Schritte zur Lösung

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

Vereinfache

(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))

Wende die Summen-/Differenzregel an:

(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)

s im pl i f y sec^{2} (2 x) - tan^{2} (2 x)

\frac{\partial}{\partial x} (- 4 e^{- x - y})

3 \frac{d y}{d x} + 12 y = 4

x \to 3 lim (\frac{x}{x - 2})

\frac{\partial}{\partial y} (y^{\frac{2}{3}})