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Beliebt Rechnen >

derivative of x-x^3sin(x)

Lösung

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

Lösung

1 - 3 x^{2} sin (x) - x^{3} cos (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

1 - (3 x^{2} sin (x) + cos (x) x^{3}) : 1 - 3 x^{2} sin (x) - x^{3} cos (x)

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

Graph

Beliebte Beispiele

inverselaplace s/((s^2+1)(s^2+2s+2))

(dy)/(dx)=y(xy^6+3)

fläche 16x,x^3,[-4,4]

(dy)/(dx)=(x+y+6)^2

integral of (6xy^2)