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Beliebt Rechnen >

derivative of 3x^2cos(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x^{2}, g = cos (2 x)

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

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

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

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

Vereinfache

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

Graph

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