derivative of (4x-4(3x^3-x^2+1))

Lösung

\frac{d}{d x} ((4 x - 4) (3 x^{3} - x^{2} + 1))

48 x^{3} - 48 x^{2} + 8 x + 4

Schritte zur Lösung

\frac{d}{d x} ((4 x - 4) (3 x^{3} - x^{2} + 1))

Wende die Produktregel an:

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

f = 4 x - 4, g = 3 x^{3} - x^{2} + 1

= \frac{d}{d x} (4 x - 4) (3 x^{3} - x^{2} + 1) + \frac{d}{d x} (3 x^{3} - x^{2} + 1) (4 x - 4)

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

\frac{d}{d x} (3 x^{3} - x^{2} + 1) = 9 x^{2} - 2 x

= 4 (3 x^{3} - x^{2} + 1) + (9 x^{2} - 2 x) (4 x - 4)

Vereinfache

4 (3 x^{3} - x^{2} + 1) + (9 x^{2} - 2 x) (4 x - 4) : 48 x^{3} - 48 x^{2} + 8 x + 4

= 48 x^{3} - 48 x^{2} + 8 x + 4

a re a y = \frac{1}{16 x ^{2}}, y = x, y = \frac{x}{18}

\int 4 x cos (4 x) d x

\int (2^{x} - x^{2})^{2} d x

l a pl a ce t r an s f or m 4 e^{(3 t)}

\frac{\partial}{\partial x} (x^{3} e^{x y} + 2 y)