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Beliebt Rechnen >

derivative of 5x^5sin(2x)

Lösung

\frac{d}{d x} (5 x^{5} sin (2 x))

Lösung

5 (5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5})

Schritte zur Lösung

\frac{d}{d x} (5 x^{5} sin (2 x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{5} sin (2 x))

Wende die Produktregel an:

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

f = x^{5}, g = sin (2 x)

= 5 (\frac{d}{d x} (x^{5}) sin (2 x) + \frac{d}{d x} (sin (2 x)) x^{5})

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= 5 (5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5})

Graph

Beliebte Beispiele

derivative of e^{(0.5x})

\frac{d}{d x} (e^{(0.5 x)})

derivative f(x)=|x-5|

d er i v a t i v e f (x) = ∣ x - 5 ∣

x^{^{''}} - 2 x - 5 = 0

(\partial)/(\partial x)(e^{kx})

\frac{\partial}{\partial x} (e^{k x})

derivative 10^{2sqrt(x)}

d er i v a t i v e 1 0^{2 x}