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Beliebt Rechnen >

(\partial)/(\partial x)(xcos(x))

Lösung

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

Lösung

cos (x) - x sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (x)

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

= cos (x) - x sin (x)

Beliebte Beispiele

integral of (2+5x)^2

\int (2 + 5 x)^{2} d x

integral of (sqrt(x)+2)

\int (x + 2) d x

derivative 3xe^{-ax}

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

5t^2y^{''}+ty^'-12y=0

5 t^{2} y^{^{''}} + t y^{^{'}} - 12 y = 0

integral of (x^2)/(sqrt(x^6-9))

\int \frac{x ^{2}}{x ^{6} - 9} d x