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Beliebt Rechnen >

derivative of xcos^3(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) x

Vereinfache

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

Graph

Beliebte Beispiele

integral from 1 to 2 of sqrt(x)ln(x)

\int_{1}^{2} x ln (x) d x

derivative of e^{(-3x})

\frac{d}{d x} (e^{(- 3 x)})

taylor e^{-3z+1}+8

t a y l or e^{- 3 z + 1} + 8

tangent x^{2/3}+y^{2/3}=5,(1,8)

t an g e n t x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5, (1, 8)

derivative f(x)=(2x-1)/(2x+1)

d er i v a t i v e f (x) = \frac{2 x - 1}{2 x + 1}