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Beliebt Rechnen >

(sin(x)+xcos(x))^'

Lösung

(sin (x) + x cos (x))^{^{'}}

Lösung

2 cos (x) - x sin (x)

Schritte zur Lösung

(sin (x) + x cos (x))^{'}

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= (sin (x))^{^{'}} + (x cos (x))^{^{'}}

(sin (x))^{'} = cos (x)

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

= cos (x) + cos (x) - x sin (x)

Vereinfache

= 2 cos (x) - x sin (x)

Graph

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