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Beliebt Rechnen >

derivative of x^2cos(4x+3)

Lösung

\frac{d}{d x} (x^{2} cos (4 x + 3))

Lösung

2 x cos (4 x + 3) - 4 x^{2} sin (4 x + 3)

Schritte zur Lösung

\frac{d}{d x} (x^{2} cos (4 x + 3))

Wende die Produktregel an:

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

f = x^{2}, g = cos (4 x + 3)

= \frac{d}{d x} (x^{2}) cos (4 x + 3) + \frac{d}{d x} (cos (4 x + 3)) x^{2}

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

\frac{d}{d x} (cos (4 x + 3)) = - sin (4 x + 3) \cdot 4

= 2 x cos (4 x + 3) + (- sin (4 x + 3) \cdot 4) x^{2}

Vereinfache

= 2 x cos (4 x + 3) - 4 x^{2} sin (4 x + 3)

Graph

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