derivative of 1/3 cos((6pix-1/2))

Lösung

\frac{d}{d x} (\frac{1}{3} cos (\frac{6 π x - 1}{2}))

- π sin (\frac{6 π x - 1}{2})

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} cos (\frac{6 π x - 1}{2}))

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (cos (\frac{6 π x - 1}{2}))

Wende die Kettenregel an:

- sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

= - sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

\frac{d}{d x} (\frac{6 π x - 1}{2}) = 3 π

= \frac{1}{3} (- sin (\frac{6 π x - 1}{2}) \cdot 3 π)

Vereinfache

\frac{1}{3} (- sin (\frac{6 π x - 1}{2}) \cdot 3 π) : - π sin (\frac{6 π x - 1}{2})

= - π sin (\frac{6 π x - 1}{2})

\int x^{7} sin (x^{8}) d x

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d er i v a t i v e e^{x} (x - 1)