derivative (3x^2+3)(2x^2+1)

Lösung

ableitung von

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

24 x^{3} + 18 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= 6 x (2 x^{2} + 1) + 4 x (3 x^{2} + 3)

Vereinfache

6 x (2 x^{2} + 1) + 4 x (3 x^{2} + 3) : 24 x^{3} + 18 x

= 24 x^{3} + 18 x

\int - \frac{y}{x ^{2} + y ^{2}} d x

x \to 2 lim (x^{3} - 8)

y^{^{'}} (t) = (y + 1) (y - 1), y (0) = 3

im pl i c i t \frac{d y}{d x}, (2 x + 3)^{4} = 3 y^{4}

d er i v a t i v e f (x) = 5 x^{2} - 2 x + 5