derivative f(x)=(3x+1)(x^2-2)

Lösung

ableitung von

f (x) = (3 x + 1) (x^{2} - 2)

9 x^{2} + 2 x - 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x + 1, g = x^{2} - 2

= \frac{d}{d x} (3 x + 1) (x^{2} - 2) + \frac{d}{d x} (x^{2} - 2) (3 x + 1)

\frac{d}{d x} (3 x + 1) = 3

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

= 3 (x^{2} - 2) + 2 x (3 x + 1)

Vereinfache

3 (x^{2} - 2) + 2 x (3 x + 1) : 9 x^{2} + 2 x - 6

= 9 x^{2} + 2 x - 6

\int \frac{4}{x ^{2} - 4 x + 13} d x

\int_{0}^{5} \frac{1}{x - 3} d x

x \to 2 lim (x^{2} - 7 x + 12)

x \to 0 lim (\frac{9 sin ( 1 )}{1})

\frac{d y}{d x} + 2 x y = 9 x