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

Lösung

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

3 (12 x^{3} - 15 x^{2} + 2 x - 6)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (3 x^{2} + x + 3) = 6 x + 1

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

= 3 ((6 x + 1) (x - 2) x + (2 x - 2) (3 x^{2} + x + 3))

Multipliziere aus

(6 x + 1) (x - 2) x + (2 x - 2) (3 x^{2} + x + 3) : 12 x^{3} - 15 x^{2} + 2 x - 6

= 3 (12 x^{3} - 15 x^{2} + 2 x - 6)

\frac{d}{d x} (6 x^{2} + 5 x)

4 y^{^{''}} - 4 y^{^{'}} + 26 y = 0

ma c l a u r in ln (x + 1)

\int \frac{4 x}{2 + 2 x ^{2}} d x

\int \frac{ln ( 6 x )}{x} d x