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Beliebt Rechnen >

derivative 5xsin(x^2)

Lösung

ableitung von

5 x sin (x^{2})

Lösung

5 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Schritte zur Lösung

\frac{d}{d x} (5 x sin (x^{2}))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x sin (x^{2}))

Wende die Produktregel an:

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

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

= 5 (\frac{d x}{d x} sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) x)

\frac{d x}{d x} = 1

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

= 5 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Vereinfache

5 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 5 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 5 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

Graph

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