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Beliebt Rechnen >

(x^3*cos(x))^'

Lösung

(x^{3} \cdot cos (x))^{^{'}}

Lösung

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

Schritte zur Lösung

(x^{3} cos (x))^{'}

Wende die Produktregel an:

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

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

= (x^{3})^{^{'}} cos (x) + (cos (x))^{^{'}} x^{3}

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

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

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

Vereinfache

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

Graph

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