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

Lösung

ableitung von

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

24 x^{2} - 12 x + 12

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

4 x (4 x - 3) + 4 (2 x^{2} + 3) : 24 x^{2} - 12 x + 12

= 24 x^{2} - 12 x + 12

d er i v a t i v e \frac{x}{6 + x}

t an g e n t 9 x - 2 x^{2}

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

in v erse l a pl a ce \frac{4 s - 1}{s ^{2} ( s + 1 ) ^{3}}

x \to + 5 lim (\frac{x + 1}{x - 5})