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Beliebt Rechnen >

derivative of sin^3(xcos(x))

Lösung

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

Lösung

3 sin^{2} (x) - 4 sin^{4} (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x)

Vereinfache

3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x) : 3 sin^{2} (x) - 4 sin^{4} (x)

= 3 sin^{2} (x) - 4 sin^{4} (x)

Graph

Beliebte Beispiele

limit as x approaches-5+of (x-3)/(x+5)

x \to - 5 + lim (\frac{x - 3}{x + 5})

derivative (1+3x)(6-5x)

d er i v a t i v e (1 + 3 x) (6 - 5 x)

derivative y=(10)/(x^3)

d er i v a t i v e y = \frac{10}{x ^{3}}

(4xy^2+4y)dx+(4x^2y+4x)dy=0

(4 x y^{2} + 4 y) d x + (4 x^{2} y + 4 x) d y = 0

wurzeln von acos(t)

roo t s a cos (t)