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Beliebt Rechnen >

derivative of xcos(5x)

Lösung

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

Lösung

cos (5 x) - 5 x sin (5 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (5 x)

= \frac{d x}{d x} cos (5 x) + \frac{d}{d x} (cos (5 x)) x

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

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= 1 \cdot cos (5 x) + (- sin (5 x) \cdot 5) x

Vereinfache

= cos (5 x) - 5 x sin (5 x)

Graph

Beliebte Beispiele

limit as x approaches 1 of 9-4x^2

x \to 1 lim (9 - 4 x^{2})

fläche x=6y^2,x=4+5y^2

a re a x = 6 y^{2}, x = 4 + 5 y^{2}

limit as x approaches-6+of x^2+6

x \to - 6 + lim (x^{2} + 6)

xy^'-2y=-2x^2-x+1

x y^{^{'}} - 2 y = - 2 x^{2} - x + 1

derivative of (2x+7^2)

\frac{d}{d x} ((2 x + 7)^{2})