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Beliebt Rechnen >

derivative of 1/3 sin^3(x)

Lösung

\frac{d}{d x} (\frac{1}{3} sin^{3} (x))

Lösung

sin^{2} (x) cos (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} sin^{3} (x))

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (sin^{3} (x))

Wende die Kettenregel an:

3 (sin (x))^{2} \frac{d}{d x} (sin (x))

= 3 (sin (x))^{2} \frac{d}{d x} (sin (x))

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

= \frac{1}{3} \cdot 3 (sin (x))^{2} cos (x)

Vereinfache

\frac{1}{3} \cdot 3 sin^{2} (x) cos (x) : sin^{2} (x) cos (x)

= sin^{2} (x) cos (x)

Graph

Beliebte Beispiele

integral of ycos(xy)

\int y cos (x y) d x

derivative of 3sec^2(x)

\frac{d}{d x} (3 sec^{2} (x))

(dy)/(dx)=cos(5x)

\frac{d y}{d x} = cos (5 x)

derivative tan(u)

d er i v a t i v e tan (u)

derivative 100(1+Ae^{-t})^{-1}

d er i v a t i v e 100 (1 + A e^{- t})^{- 1}