derivative (x^2-3)(x^3-2x)

Lösung

ableitung von

(x^{2} - 3) (x^{3} - 2 x)

5 x^{4} - 15 x^{2} + 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} - 3, g = x^{3} - 2 x

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

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

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

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

Vereinfache

2 x (x^{3} - 2 x) + (3 x^{2} - 2) (x^{2} - 3) : 5 x^{4} - 15 x^{2} + 6

= 5 x^{4} - 15 x^{2} + 6

\int_{3}^{9} 1 + x^{4} + 2 x^{2} d x

d er i v a t i v e y = 3 1 + 7 x

\frac{d}{d x} (18 x^{2})

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

\int_{1}^{4} x^{2} + \frac{1}{4 x ^{2}} d x