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Beliebt Rechnen >

derivative of a(sin(x-xcos(x)))

Lösung

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

Lösung

a x sin (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

= a (\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)

= a (cos (x) - (cos (x) - x sin (x)))

Vereinfache

= a x sin (x)

Graph

Beliebte Beispiele

integral of xln(x-2)

\int x ln (x - 2) d x

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

\int \frac{e ^{x}}{1 - e ^{x}} d x

derivative of xsqrt(3)-2x^2

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

integral from 0 to 1 of 4(1+sqrt(x))^7

\int_{0}^{1} 4 (1 + x)^{7} d x

derivative of 800sqrt(x^2-0.1x)

\frac{d}{d x} (800 x^{2} - 0.1 x)