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Beliebt Rechnen >

derivative of x(2-x)

Lösung

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

Lösung

2 - 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = 2 - x

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

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

\frac{d}{d x} (2 - x) = - 1

= 1 \cdot (2 - x) + (- 1) x

Vereinfache

1 \cdot (2 - x) + (- 1) x : 2 - 2 x

= 2 - 2 x

Graph

Beliebte Beispiele

integral of (5x)/(e^{2x)}

\int \frac{5 x}{e ^{2 x}} d x

integral of (7x+8)/(7x^2+16x+9)

\int \frac{7 x + 8}{7 x ^{2} + 16 x + 9} d x

derivative of 1/(x^{11})

\frac{d}{d x} (\frac{1}{x ^{11}})

limit as x approaches 3+of (18-6x)/(3-x)

x \to 3 + lim (\frac{18 - 6 x}{3 - x})

derivative of 2\sqrt[3]{x^7}

\frac{d}{d x} (2 3 x^{7})