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Beliebt Rechnen >

derivative 2cos^2(t/2)

Lösung

ableitung von

2 cos^{2} (\frac{t}{2})

Lösung

- sin (t)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d t} (cos^{2} (\frac{t}{2}))

Wende die Kettenregel an:

2 cos (\frac{t}{2}) \frac{d}{d t} (cos (\frac{t}{2}))

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

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

= 2 \cdot 2 cos (\frac{t}{2}) (- sin (\frac{t}{2}) \frac{1}{2})

Vereinfache

2 \cdot 2 cos (\frac{t}{2}) (- sin (\frac{t}{2}) \frac{1}{2}) : - sin (t)

= - sin (t)

Graph

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