derivative of 2(cos(x/2-(sqrt(2))/2))

Lösung

\frac{d}{d x} (2 (cos (\frac{x}{2}) - \frac{2}{2}))

- sin (\frac{x}{2})

Schritte zur Lösung

\frac{d}{d x} (2 (cos (\frac{x}{2}) - \frac{2}{2}))

Vereinfache

2 (cos (\frac{x}{2}) - \frac{2}{2}) : 2 (cos (\frac{x}{2}) - \frac{1}{2})

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (\frac{1}{2}) = 0

= 2 (- sin (\frac{x}{2}) \frac{1}{2} - 0)

Vereinfache

2 (- sin (\frac{x}{2}) \frac{1}{2} - 0) : - sin (\frac{x}{2})

= - sin (\frac{x}{2})

d er i v a t i v e f (x) = 3 1 + 4 x

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