derivative of (x^3+3x(2x+4))

Lösung

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

8 x^{3} + 12 x^{2} + 12 x + 12

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

(3 x^{2} + 3) (2 x + 4) + 2 (x^{3} + 3 x) : 8 x^{3} + 12 x^{2} + 12 x + 12

= 8 x^{3} + 12 x^{2} + 12 x + 12

x \to 4 lim (x^{2} + 2 x + 2)

\frac{d}{d x} (\frac{- x + y - 2}{x - 2})

\frac{d}{d x} (lo g_{2} (\frac{x ^{2}}{x - 1}))

x \to + 3 lim (\frac{π + x}{4})

\frac{d}{d θ} (sin (θ) + csc (θ))