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Beliebt Rechnen >

derivative of sin^5(x/3)

Lösung

\frac{d}{d x} (sin^{5} (\frac{x}{3}))

Lösung

\frac{5}{3} sin^{4} (\frac{x}{3}) cos (\frac{x}{3})

Schritte zur Lösung

\frac{d}{d x} (sin^{5} (\frac{x}{3}))

Wende die Kettenregel an:

5 (sin (\frac{x}{3}))^{4} \frac{d}{d x} (sin (\frac{x}{3}))

= 5 (sin (\frac{x}{3}))^{4} \frac{d}{d x} (sin (\frac{x}{3}))

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

= 5 (sin (\frac{x}{3}))^{4} cos (\frac{x}{3}) \frac{1}{3}

Vereinfache

5 sin^{4} (\frac{x}{3}) cos (\frac{x}{3}) \frac{1}{3} : \frac{5}{3} sin^{4} (\frac{x}{3}) cos (\frac{x}{3})

= \frac{5}{3} sin^{4} (\frac{x}{3}) cos (\frac{x}{3})

Graph

Beliebte Beispiele

integral of x/((x+4)^2)

\int \frac{x}{( x + 4 ) ^{2}} d x

limit as t approaches 3 of 2t^{-1}

t \to 3 lim (2 t^{- 1})

integral of ((x^2-x+28))/(x^3+7x)

\int \frac{( x ^{2} - x + 28 )}{x ^{3} + 7 x} d x

y^'(t)=(y-1)(y+1),y(0)=3

y^{^{'}} (t) = (y - 1) (y + 1), y (0) = 3

integral of sin(1-3x)

\int sin (1 - 3 x) d x