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Beliebt Rechnen >

derivative (6x^3+2x+9)(x^2+6)

Lösung

ableitung von

(6 x^{3} + 2 x + 9) (x^{2} + 6)

Lösung

30 x^{4} + 114 x^{2} + 18 x + 12

Schritte zur Lösung

\frac{d}{d x} ((6 x^{3} + 2 x + 9) (x^{2} + 6))

Wende die Produktregel an:

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

f = 6 x^{3} + 2 x + 9, g = x^{2} + 6

= \frac{d}{d x} (6 x^{3} + 2 x + 9) (x^{2} + 6) + \frac{d}{d x} (x^{2} + 6) (6 x^{3} + 2 x + 9)

\frac{d}{d x} (6 x^{3} + 2 x + 9) = 18 x^{2} + 2

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

= (18 x^{2} + 2) (x^{2} + 6) + 2 x (6 x^{3} + 2 x + 9)

Vereinfache

(18 x^{2} + 2) (x^{2} + 6) + 2 x (6 x^{3} + 2 x + 9) : 30 x^{4} + 114 x^{2} + 18 x + 12

= 30 x^{4} + 114 x^{2} + 18 x + 12

Graph

Beliebte Beispiele

x y^{^{'}} + y = 2 x y^{2}

integral of (x(3-5x))/((3x-1)(x-1)^2)

\int \frac{x ( 3 - 5 x )}{( 3 x - 1 ) ( x - 1 ) ^{2}} d x

fläche 7x+y^2=15,x=2y

a re a 7 x + y^{2} = 15, x = 2 y

fläche y=cos(3x),(0.4,0.6)

a re a y = cos (3 x), (0.4, 0.6)

limit as x approaches-3 of 2x+5

x \to - 3 lim (2 x + 5)