derivative of 1/2 cos^2(x/2)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} ((4 x^{3} - 7 x)^{7})

\int x 2 x - x^{2} d x

\int (\frac{8 + 5 x}{1 + x ^{2}}) d x

\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)