erweitern Dx[\sqrt[3]{6x^3+3}(5x^2-4)]

Lösung

erweitern

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

5 D x^{3} 3 6 x^{3} + 3 - 4 D x 3 6 x^{3} + 3

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = D x 3 6 x^{3} + 3, b = 5 x^{2}, c = 4

= D x 3 6 x^{3} + 3 \cdot 5 x^{2} - D x 3 6 x^{3} + 3 \cdot 4

= 5 D x^{2} x 3 6 x^{3} + 3 - 4 D x 3 6 x^{3} + 3

5 D x^{2} x 3 6 x^{3} + 3 = 5 D x^{3} 3 6 x^{3} + 3

= 5 D x^{3} 3 6 x^{3} + 3 - 4 D x 3 6 x^{3} + 3

e x p an d (2 x^{2} + 3 x) (x - 1)

s im pl i f y x^{2} (x - \frac{1}{2})

e x p an d \frac{2 ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{2}}

e x p an d \frac{2 x}{( x + 3 ) ( 3 x + 1 )}

e x p an d \frac{d}{d x} ((x) (x^{2} - 7 x + 1)) - (2 x - 7) (x + 9)