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Beliebt Rechnen >

derivative y=xcos(x)

Lösung

ableitung von

y = 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

fläche x=63-7y^2,x=7y^2-63

a re a x = 63 - 7 y^{2}, x = 7 y^{2} - 63

derivative t^3-t

d er i v a t i v e t^{3} - t

derivative of sqrt(1-x^2)-xarccos(x)

\frac{d}{d x} (1 - x^{2} - x arccos (x))

y(dy)/(dx)=-8cos(pix)

y \frac{d y}{d x} = - 8 cos (π x)

(\partial)/(\partial x)(csc^2(x))

\frac{\partial}{\partial x} (csc^{2} (x))