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Beliebt Rechnen >

derivative of 4sin(x/2)

Lösung

\frac{d}{d x} (4 sin (\frac{x}{2}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (4 sin (\frac{x}{2}))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (sin (\frac{x}{2}))

Wende die Kettenregel an:

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

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

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

= 4 cos (\frac{x}{2}) \frac{1}{2}

Vereinfache

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

= 2 cos (\frac{x}{2})

Graph

Beliebte Beispiele

integral from-infinity to 0 of 1/(7-9x)

\int_{- \infty}^{0} \frac{1}{7 - 9 x} d x

derivative of 5e^{-2x}+4

\frac{d}{d x} (5 e^{- 2 x} + 4)

derivative of 8^{4-x^2}

\frac{d}{d x} (8^{4 - x^{2}})

steigung (x^2-35)^6

s l o p e (x^{2} - 35)^{6}

derivative of 1/(sin(x+cos(x)))

\frac{d}{d x} (\frac{1}{sin ( x ) + cos ( x )})