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Beliebt Rechnen >

derivative of sqrt(5)x^5{f}(x)

Lösung

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

Lösung

5 (5 x^{4} f (x) + \frac{d}{d x} (f (x)) x^{5})

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

Beliebte Beispiele

y^'=e^{t+y},y(0)=0

y^{^{'}} = e^{t + y}, y (0) = 0

integral of 5e^{3x+7}

\int 5 e^{3 x + 7} d x

integral from 0 to 5 of (x^2-5x)

\int_{0}^{5} (x^{2} - 5 x) d x

sum from n=0 to infinity of (-1)^n2

n = 0 \sum \infty (- 1)^{n} 2

fläche (21)/(x^3),1,1000

a re a \frac{21}{x ^{3}}, 1, 1000