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Beliebt Rechnen >

derivative of x(cos(x))

Lösung

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

Lösung

cos (x) - x sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (x)

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

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

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

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

Vereinfache

= cos (x) - x sin (x)

Graph

Beliebte Beispiele

derivative sqrt(9x^2-1)

d er i v a t i v e 9 x^{2} - 1

derivative y=cos^4(t)-sin^4(t)

d er i v a t i v e y = cos^{4} (t) - sin^{4} (t)

limit as x approaches infinity of x^3

x \to \infty lim (x^{3})

integral of 6/(y^4)

\int \frac{6}{y ^{4}} d y

integral of (x^2)^2x^2)^2

\int (x^{2})^{2} d (x^{2})^{2}