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Beliebt Rechnen >

derivative x^6cos(x)

Lösung

ableitung von

x^{6} cos (x)

Lösung

6 x^{5} cos (x) - x^{6} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{6} cos (x))

Wende die Produktregel an:

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

f = x^{6}, g = cos (x)

= \frac{d}{d x} (x^{6}) cos (x) + \frac{d}{d x} (cos (x)) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} cos (x) + (- sin (x)) x^{6}

Vereinfache

= 6 x^{5} cos (x) - x^{6} sin (x)

Graph

Beliebte Beispiele

derivative y(s)= 1/(s+ke^s)

d er i v a t i v e y (s) = \frac{1}{s + k e ^{s}}

sum from n=1 to infinity of arcsin(n)

n = 1 \sum \infty arcsin (n)

y^{''}+4y^'-5y=e^{3x}

y^{^{''}} + 4 y^{^{'}} - 5 y = e^{3 x}

derivative of (x^9/(45))

\frac{d}{d x} (\frac{x ^{9}}{45})

fläche y=6x,y=6x^2

a re a y = 6 x, y = 6 x^{2}