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Beliebt Rechnen >

(\partial)/(\partial x)(xsin(x))

Lösung

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

Lösung

sin (x) + x cos (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (x)

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

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

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

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

Vereinfache

= sin (x) + x cos (x)

Beliebte Beispiele

(\partial)/(\partial x)(y^{x^7})

\frac{\partial}{\partial x} (y^{x^{7}})

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

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

a re a x^{2}, 4 x

fläche y=1+2sqrt(x),y=(3+x)/3

a re a y = 1 + 2 x, y = \frac{3 + x}{3}

fläche sqrt(x), x/2

a re a x, \frac{x}{2}