derivative y= 1/3 cos((6pix-1)/2)

Lösung

ableitung von

y = \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})

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