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Beliebt Rechnen >

derivative of (-x^2+2x(3x+2)(x-1))

Lösung

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

Lösung

- 12 x^{3} + 21 x^{2} - 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = - x^{2} + 2 x, g = (3 x + 2) (x - 1)

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

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

\frac{d}{d x} ((3 x + 2) (x - 1)) = 6 x - 1

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

Vereinfache

(- 2 x + 2) (3 x + 2) (x - 1) + (6 x - 1) (- x^{2} + 2 x) : - 12 x^{3} + 21 x^{2} - 4

= - 12 x^{3} + 21 x^{2} - 4

Graph

Beliebte Beispiele

tangent f(x)=3x^2,(1,3)

t an g e n t f (x) = 3 x^{2}, (1, 3)

y^{^{'}} = \frac{e ^{x}}{y}

integral from 1 to 5 of 2/x

\int_{1}^{5} \frac{2}{x} d x

limit as x approaches 0 of (20)/(1+x)

x \to 0 lim (\frac{20}{1 + x})

integral of cos(5)

\int cos (5)