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Beliebt Rechnen >

(xcos(x))^'

Lösung

(x cos (x))^{^{'}}

Lösung

cos (x) - x sin (x)

Schritte zur Lösung

(x cos (x))^{'}

Wende die Produktregel an:

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

f = x, g = cos (x)

= x^{^{'}} cos (x) + (cos (x))^{^{'}} x

x^{'} = 1

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

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

Vereinfache

= cos (x) - x sin (x)

Graph

Beliebte Beispiele

derivative f(x)=x^3(3-x^2)

d er i v a t i v e f (x) = x^{3} (3 - x^{2})

derivative f(x)= x/(x^2-7)

d er i v a t i v e f (x) = \frac{x}{x ^{2} - 7}

integral of (2x)/((x-3)^2)

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

limit as n approaches 2 of 1/(n^2)

n \to 2 lim (\frac{1}{n ^{2}})

limit as x approaches 2+of sqrt(x^2-4)

x \to 2 + lim (x^{2} - 4)