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Beliebt Rechnen >

(sin(x)sin(2x)sin(3x))^'

Lösung

(sin (x) sin (2 x) sin (3 x))^{^{'}}

Lösung

cos (x) sin (2 x) sin (3 x) + (cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)) sin (x)

Schritte zur Lösung

(sin (x) sin (2 x) sin (3 x))^{'}

Wende die Produktregel an:

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

f = sin (x), g = sin (2 x) sin (3 x)

= (sin (x))^{^{'}} sin (2 x) sin (3 x) + (sin (2 x) sin (3 x))^{^{'}} sin (x)

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

(sin (2 x) sin (3 x))^{'} = cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)

= cos (x) sin (2 x) sin (3 x) + (cos (2 x) \cdot 2 sin (3 x) + cos (3 x) \cdot 3 sin (2 x)) sin (x)

Graph

Beliebte Beispiele

derivative y=e^xsin(2x)

d er i v a t i v e y = e^{x} sin (2 x)

limit as x approaches 0+of xln(sin(x))

x \to 0 + lim (x ln (sin (x)))

integral of 1/(sqrt(5x-2))

\int \frac{1}{5 x - 2} d x

(dr)/(dθ)=8(cos(θ/3))^3

\frac{d r}{d θ} = 8 (cos (\frac{θ}{3}))^{3}

limit as x approaches 0+of (e^x+x)^{2/x}

x \to 0 + lim ((e^{x} + x)^{\frac{2}{x}})