derivative y=(4x^2+3)(2x-3)

Lösung

ableitung von

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

24 x^{2} - 24 x + 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

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

= 8 x (2 x - 3) + 2 (4 x^{2} + 3)

Vereinfache

8 x (2 x - 3) + 2 (4 x^{2} + 3) : 24 x^{2} - 24 x + 6

= 24 x^{2} - 24 x + 6

\int 18 arctan (x) d x

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

t an g e n t f (x) = x^{4} + 2 \cdot e^{x}, at x = 0

\int 5 sin (\frac{nπ x}{4}) d x

\int 7^{n} ln (7) d n