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Beliebt Vorkalkül >

derivative 2xsin(x)

Lösung

ableitung von

2 x sin (x)

Lösung

2 (sin (x) + x cos (x))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = sin (x)

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 2 (sin (x) + x cos (x))

Graph

Beliebte Beispiele

derivative f(x)=t^2ln(e^{2t}+1)

d er i v a t i v e f (x) = t^{2} ln (e^{2 t} + 1)

polar (sqrt(2),-sqrt(2))

p o l a r (2, - 2)

steigung 2x+4y=7

s l o p e 2 x + 4 y = 7

derivative f(x)=x^2ln(x)

d er i v a t i v e f (x) = x^{2} ln (x)

derivative f(x)= 1/(x-1)

d er i v a t i v e f (x) = \frac{1}{x - 1}