derivative of 2sin(1/2 x)

Lösung

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

cos (\frac{x}{2})

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

= 2 \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}

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

Vereinfache

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

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

\int - 2 x d x

d er i v a t i v e y = e^{x^{2} + 9 x + 4}

a re a y = 3 x^{2}, y = 16 - x^{2}

\int \frac{2}{5 x 9 - 49 x ^{2}} d x

\frac{d x}{d t} = sin (2 t) - 3 x