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Beliebt Rechnen >

derivative x^5sin(x)

Lösung

ableitung von

x^{5} sin (x)

Lösung

5 x^{4} sin (x) + cos (x) x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} sin (x))

Wende die Produktregel an:

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

f = x^{5}, g = sin (x)

= \frac{d}{d x} (x^{5}) sin (x) + \frac{d}{d x} (sin (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} sin (x) + cos (x) x^{5}

Graph

Beliebte Beispiele

limit as x approaches 0 of (1-cos^2(3x))/(x^2)

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

derivative f(x)=3arcsin(x^4)

d er i v a t i v e f (x) = 3 arcsin (x^{4})

integral from 0 to 1 of 3x^2

\int_{0}^{1} 3 x^{2} d x

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

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

integral of 10sinh(4x-ln(2))

\int 10 sinh (4 x - ln (2)) d x