derivative of-6sin(pi/(12x)+18)

Lösung

\frac{d}{d x} (- 6 sin (\frac{π}{12} x) + 18)

- \frac{π}{2} cos (\frac{π x}{12})

Schritte zur Lösung

\frac{d}{d x} (- 6 sin (\frac{π}{12} x) + 18)

Vereinfache

- 6 sin (\frac{π}{12} x) + 18 : - 6 sin (\frac{π x}{12}) + 18

= \frac{d}{d x} (- 6 sin (\frac{π x}{12}) + 18)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (6 sin (\frac{π x}{12})) + \frac{d}{d x} (18)

\frac{d}{d x} (6 sin (\frac{π x}{12})) = \frac{π}{2} cos (\frac{π x}{12})

\frac{d}{d x} (18) = 0

= - \frac{π}{2} cos (\frac{π x}{12}) + 0

Vereinfache

= - \frac{π}{2} cos (\frac{π x}{12})

\int_{0}^{\frac{π}{2}} cos^{5} (y) d y

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