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Beliebt Rechnen >

derivative f(x)=sin(x)+xcos(x)

Lösung

ableitung von

f (x) = sin (x) + x cos (x)

Lösung

2 cos (x) - x sin (x)

Schritte zur Lösung

\frac{d}{d x} (sin (x) + x cos (x))

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative of 2\sqrt[3]{x^4}

\frac{d}{d x} (2 3 x^{4})

integral of 9sin^3(x)cos^7(x)

\int 9 sin^{3} (x) cos^{7} (x) d x

integral from 0 to infinity of x

\int_{0}^{\infty} x d x

derivative of axe^{-5x}

\frac{d}{d x} (a x e^{- 5 x})

integral of 4sin(2x)

\int 4 sin (2 x) d x