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Beliebt Rechnen >

d/(dt)((sin(t)+cos(t))^2)

Lösung

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

Lösung

2 cos (2 t)

Schritte zur Lösung

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

Vereinfache

(sin (t) + cos (t))^{2} : 1 + sin (2 t)

= \frac{d}{d t} (1 + sin (2 t))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (1) + \frac{d}{d t} (sin (2 t))

\frac{d}{d t} (1) = 0

\frac{d}{d t} (sin (2 t)) = cos (2 t) \cdot 2

= 0 + cos (2 t) \cdot 2

Vereinfache

= 2 cos (2 t)

Graph

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