derivative x^2sin(sqrt(x))

Lösung

ableitung von

x^{2} sin (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

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