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Beliebt Rechnen >

derivative derivative of xsin(x)

Lösung

ableitung von

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

Lösung

sin (x) + x cos (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (x)

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

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

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

= 1 \cdot sin (x) + cos (x) x

Vereinfache

= sin (x) + x cos (x)

Graph

Beliebte Beispiele

integral of (1/((x-x^2)))

\int (\frac{1}{( x - x ^{2} )}) d x

derivative derivative of x/a

d er i v a t i v e \frac{d}{d x} (\frac{x}{a})

derivative derivative of 2e^{-2x}

d er i v a t i v e \frac{d}{d x} (2 e^{- 2 x})

derivative d/(dy)(y^2)

d er i v a t i v e \frac{d}{d y} (y^{2})

integral (-1)/((e^x))

in t e g r a l \frac{- 1}{( e ^{x} )}