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Beliebt Rechnen >

derivative-sin(x^2)(2x)

Lösung

ableitung von

- sin (x^{2}) (2 x)

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

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