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

Lösung

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

\frac{1}{4} (2 x sin (x - 2) + cos (x - 2) x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (x^{2} sin (x - 2))

Wende die Produktregel an:

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

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

= \frac{1}{4} (\frac{d}{d x} (x^{2}) sin (x - 2) + \frac{d}{d x} (sin (x - 2)) x^{2})

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

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

= \frac{1}{4} (2 x sin (x - 2) + cos (x - 2) x^{2})

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