derivative of sin^3(x/3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{x}{x + 2} d x

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