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Beliebt Rechnen >

derivative of (x^2+x(6-x))

Lösung

\frac{d}{d x} ((x^{2} + x) (6 - x))

Lösung

- 3 x^{2} + 10 x + 6

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + x) (6 - x))

Wende die Produktregel an:

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

f = x^{2} + x, g = 6 - x

= \frac{d}{d x} (x^{2} + x) (6 - x) + \frac{d}{d x} (6 - x) (x^{2} + x)

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

\frac{d}{d x} (6 - x) = - 1

= (2 x + 1) (6 - x) + (- 1) (x^{2} + x)

Vereinfache

(2 x + 1) (6 - x) + (- 1) (x^{2} + x) : - 3 x^{2} + 10 x + 6

= - 3 x^{2} + 10 x + 6

Graph

Beliebte Beispiele

integral of 1/(sqrt(7x+6))

\int \frac{1}{7 x + 6} d x

slopeintercept (2,4),(5,13)

s l o p e in t erce pt (2, 4), (5, 13)

integral of (1/3)^x

\int (\frac{1}{3})^{x} d x

limit as x approaches 4 of x/(x+1)

x \to 4 lim (\frac{x}{x + 1})

fläche f(x)=1-e^{-x/3},2,3

a re a f (x) = 1 - e^{- \frac{x}{3}}, 2, 3