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Beliebt Rechnen >

derivative f(x)=(x^2-5x+8)(3x^2-2)

Lösung

ableitung von

f (x) = (x^{2} - 5 x + 8) (3 x^{2} - 2)

Lösung

12 x^{3} - 45 x^{2} + 44 x + 10

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 5 x + 8) (3 x^{2} - 2))

Wende die Produktregel an:

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

f = x^{2} - 5 x + 8, g = 3 x^{2} - 2

= \frac{d}{d x} (x^{2} - 5 x + 8) (3 x^{2} - 2) + \frac{d}{d x} (3 x^{2} - 2) (x^{2} - 5 x + 8)

\frac{d}{d x} (x^{2} - 5 x + 8) = 2 x - 5

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

= (2 x - 5) (3 x^{2} - 2) + 6 x (x^{2} - 5 x + 8)

Vereinfache

(2 x - 5) (3 x^{2} - 2) + 6 x (x^{2} - 5 x + 8) : 12 x^{3} - 45 x^{2} + 44 x + 10

= 12 x^{3} - 45 x^{2} + 44 x + 10

Graph

Beliebte Beispiele

derivative of 1/(x+y)

\frac{d}{d x} (\frac{1}{x + y})

integral of 6x+12xln(8x)

\int 6 x + 12 x ln (8 x) d x

integral of (x^{-2})

\int (x^{- 2}) d x

(10y^2-xy)dx+x^2dy=0

(10 y^{2} - x y) d x + x^{2} d y = 0

limit as x approaches infinity of 6x^2

x \to \infty lim (6 x^{2})