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Beliebt Rechnen >

derivative of xcos(y)

Lösung

\frac{d}{d x} (x cos (y))

Lösung

cos (y) - x sin (y) \frac{d y}{d x}

Schritte zur Lösung

\frac{d}{d x} (x cos (y))

Wende die Produktregel an:

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

f = x, g = cos (y)

= \frac{d x}{d x} cos (y) + \frac{d}{d x} (cos (y)) x

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

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

= 1 \cdot cos (y) + (- sin (y) \frac{d y}{d x}) x

Vereinfache

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

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