derivative (4x+3)(2x^2+7x-1)

Lösung

ableitung von

(4 x + 3) (2 x^{2} + 7 x - 1)

24 x^{2} + 68 x + 17

Schritte zur Lösung

\frac{d}{d x} ((4 x + 3) (2 x^{2} + 7 x - 1))

Wende die Produktregel an:

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

f = 4 x + 3, g = 2 x^{2} + 7 x - 1

= \frac{d}{d x} (4 x + 3) (2 x^{2} + 7 x - 1) + \frac{d}{d x} (2 x^{2} + 7 x - 1) (4 x + 3)

\frac{d}{d x} (4 x + 3) = 4

\frac{d}{d x} (2 x^{2} + 7 x - 1) = 4 x + 7

= 4 (2 x^{2} + 7 x - 1) + (4 x + 7) (4 x + 3)

Vereinfache

4 (2 x^{2} + 7 x - 1) + (4 x + 7) (4 x + 3) : 24 x^{2} + 68 x + 17

= 24 x^{2} + 68 x + 17

\int x^{2} - 21 d x

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

d er i v a t i v e \frac{x ^{2} - 2 x}{x}

\int_{1}^{13} 4 x^{- 2} d x

\int \frac{1}{x 49 x ^{2} + 1} d x