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Beliebt Rechnen >

derivative derivative of 2xy

Lösung

ableitung von

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

Lösung

2 (y + x \frac{d y}{d x})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = y

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

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

= 2 (1 \cdot y + \frac{d y}{d x} x)

Vereinfache

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

Beliebte Beispiele

arclength f(x)=x^2+2x,0<x<6

a rc l e n g t h f (x) = x^{2} + 2 x, 0 < x < 6

derivative derivative of tan(3x)

d er i v a t i v e \frac{d}{d x} (tan (3 x))

derivative of f(x)=e^{4x}

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

derivative of y=6x

\frac{d}{d x} y = 6 x

derivative derivative of 7x

d er i v a t i v e \frac{d}{d x} (7 x)