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Beliebt Rechnen >

derivative 2x*cos(x^2)

Lösung

ableitung von

2 x \cdot cos (x^{2})

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

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