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Beliebt Rechnen >

derivative of x^3sin(5x)

Lösung

\frac{d}{d x} (x^{3} sin (5 x))

Lösung

3 x^{2} sin (5 x) + cos (5 x) \cdot 5 x^{3}

Schritte zur Lösung

\frac{d}{d x} (x^{3} sin (5 x))

Wende die Produktregel an:

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

f = x^{3}, g = sin (5 x)

= \frac{d}{d x} (x^{3}) sin (5 x) + \frac{d}{d x} (sin (5 x)) x^{3}

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 3 x^{2} sin (5 x) + cos (5 x) \cdot 5 x^{3}

Graph

Beliebte Beispiele

derivative of x^4-4x^3+4x^2

integral of (1+x+x^2)ln(x)

derivative y=-csc(x)-sin(x)

y^{''}-4y^'-5y=-3e^4t,y(0)=0,y^'(0)=0

integral from 1 to x of (1/(t^3+1))