derivative (5x^2-2x+4)(4x^2+3x-6)

Lösung

ableitung von

(5 x^{2} - 2 x + 4) (4 x^{2} + 3 x - 6)

80 x^{3} + 21 x^{2} - 40 x + 24

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} - 2 x + 4) (4 x^{2} + 3 x - 6))

Wende die Produktregel an:

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

f = 5 x^{2} - 2 x + 4, g = 4 x^{2} + 3 x - 6

= \frac{d}{d x} (5 x^{2} - 2 x + 4) (4 x^{2} + 3 x - 6) + \frac{d}{d x} (4 x^{2} + 3 x - 6) (5 x^{2} - 2 x + 4)

\frac{d}{d x} (5 x^{2} - 2 x + 4) = 10 x - 2

\frac{d}{d x} (4 x^{2} + 3 x - 6) = 8 x + 3

= (10 x - 2) (4 x^{2} + 3 x - 6) + (8 x + 3) (5 x^{2} - 2 x + 4)

Vereinfache

(10 x - 2) (4 x^{2} + 3 x - 6) + (8 x + 3) (5 x^{2} - 2 x + 4) : 80 x^{3} + 21 x^{2} - 40 x + 24

= 80 x^{3} + 21 x^{2} - 40 x + 24

\int - x^{2} + 6 d x

x \to 5 lim (\frac{1}{( x - 5 )})

\frac{\partial}{\partial x} (x^{2} \frac{1}{y + 1})

t an g e n t y = \frac{5 x}{x - 3}, (4, 20)

\int (x^{2} + 2 y) d x