derivative of 3x(x^2-x+1(5x-3))

Lösung

\frac{d}{d x} (3 x (x^{2} - x + 1) (5 x - 3))

3 (20 x^{3} - 24 x^{2} + 16 x - 3)

Schritte zur Lösung

\frac{d}{d x} (3 x (x^{2} - x + 1) (5 x - 3))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (x (x^{2} - x + 1) (5 x - 3))

Wende die Produktregel an:

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

f = x, g = (x^{2} - x + 1) (5 x - 3)

= 3 (\frac{d x}{d x} (x^{2} - x + 1) (5 x - 3) + \frac{d}{d x} ((x^{2} - x + 1) (5 x - 3)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} - x + 1) (5 x - 3)) = 15 x^{2} - 16 x + 8

= 3 (1 \cdot (x^{2} - x + 1) (5 x - 3) + (15 x^{2} - 16 x + 8) x)

Vereinfache

3 (1 \cdot (x^{2} - x + 1) (5 x - 3) + (15 x^{2} - 16 x + 8) x) : 3 (20 x^{3} - 24 x^{2} + 16 x - 3)

= 3 (20 x^{3} - 24 x^{2} + 16 x - 3)

\frac{d y}{d t} = - 2 y, y (0) = \frac{1}{10}

t an g e n t x^{2} - 8

\frac{d}{d x} (sin (2 x) cos (2 x))

t an g e n t f (x) = x^{3}, at x = 6

\int - 9 x d x