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

Lösung

\frac{d}{d x} ((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

d er i v a t i v e 2 x^{2} - 2 x + 4

y^{^{'''}} - 9 y^{^{''}} + 18 y^{^{'}} = e^{e^{- 3 x}}

\frac{\partial}{\partial t} (\frac{r}{t})

d er i v a t i v e \frac{( m v ^{2} )}{r}

\frac{d y}{d x} = x y + 2 x