derivative of 1/2 cos(x/2)

Lösung

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

- \frac{1}{4} sin (\frac{x}{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2} (- sin (\frac{x}{2}) \frac{1}{2}) : - \frac{1}{4} sin (\frac{x}{2})

= - \frac{1}{4} sin (\frac{x}{2})

y^{^{'}} = y^{2} + y

\frac{d}{d x} ((3 x + 2)^{6})

\int_{- 7}^{7} \frac{1}{x} d x

t an g e n t y = \frac{x}{9 + x ^{2}}, (0, 0)

\int 3 + x \cdot (x + 1)^{2} d x