derivative of 4x^2*sin(4x)

Lösung

\frac{d}{d x} (4 x^{2} \cdot sin (4 x))

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

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} sin (4 x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} sin (4 x))

Wende die Produktregel an:

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

f = x^{2}, g = sin (4 x)

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

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

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

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

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