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Beliebt Rechnen >

derivative y=2xsin(x)

Lösung

ableitung von

y = 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

limit as x approaches 0 of (4x)/(|x|)

x \to 0 lim (\frac{4 x}{∣ x ∣})

y^{^{''}} - 8 y^{^{'}} = 5 t

y^{''}+4y^'+4y=12t+16,y(0)=3,y^'(0)=-4

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16, y (0) = 3, y^{^{'}} (0) = - 4

derivative of (2^0/(3^1+0))

\frac{d}{d x} (\frac{2 ^{0}}{3 ^{1} + 0})

y^'-2y=0,y(0)=2

y^{^{'}} - 2 y = 0, y (0) = 2