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Beliebt Rechnen >

derivative of cos(x/3 sin(x))

Lösung

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

Lösung

- \frac{1}{3} sin (\frac{x}{3}) sin (x) + cos (x) cos (\frac{x}{3})

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (\frac{x}{3}), g = sin (x)

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

d/(dt)(1/(2sqrt(t)))

\frac{d}{d t} (\frac{1}{2 t})

integral of-2cos(6x)

\int - 2 cos (6 x) d x

derivative f(x)=8x^{15}-6x^3+1

d er i v a t i v e f (x) = 8 x^{15} - 6 x^{3} + 1

(dy)/(dt)=y^2-y

\frac{d y}{d t} = y^{2} - y

fläche x^3-10x,15x

a re a x^{3} - 10 x, 15 x