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Beliebt Rechnen >

derivative x^2*cos(x)

Lösung

ableitung von

x^{2} \cdot cos (x)

Lösung

2 x cos (x) - x^{2} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{2} cos (x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (x)

= \frac{d}{d x} (x^{2}) cos (x) + \frac{d}{d x} (cos (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x cos (x) + (- sin (x)) x^{2}

Vereinfache

= 2 x cos (x) - x^{2} sin (x)

Graph

Beliebte Beispiele

derivative of (x^3/3-1/(4x))

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{1}{4 x})

derivative of-0.5x

\frac{d}{d x} (- 0.5 x)

derivative of 5arctan(x)

\frac{d}{d x} (5 arctan (x))

integral from 3 to 6 of x/(x^2+4x+20)

\int_{3}^{6} \frac{x}{x ^{2} + 4 x + 20} d x

integral of 8x^9-3x^6+12x^3

\int 8 x^{9} - 3 x^{6} + 12 x^{3} d x