derivative of 6x^2(4x^5-3x+2)

Lösung

\frac{d}{d x} (6 x^{2} (4 x^{5} - 3 x + 2))

6 (28 x^{6} - 9 x^{2} + 4 x)

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} (4 x^{5} - 3 x + 2))

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{2} (4 x^{5} - 3 x + 2))

Wende die Produktregel an:

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

f = x^{2}, g = 4 x^{5} - 3 x + 2

= 6 (\frac{d}{d x} (x^{2}) (4 x^{5} - 3 x + 2) + \frac{d}{d x} (4 x^{5} - 3 x + 2) x^{2})

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

\frac{d}{d x} (4 x^{5} - 3 x + 2) = 20 x^{4} - 3

= 6 (2 x (4 x^{5} - 3 x + 2) + (20 x^{4} - 3) x^{2})

Multipliziere aus

2 x (4 x^{5} - 3 x + 2) + (20 x^{4} - 3) x^{2} : 28 x^{6} - 9 x^{2} + 4 x

= 6 (28 x^{6} - 9 x^{2} + 4 x)

x \to 0 + lim (x^{3} (ln (x))^{2})

d er i v a t i v e y = x (1 + x^{2})^{10}

x \to 0 - lim (\frac{x}{x})

\int (3 y - 4 y^{3})^{3} d y

t an g e n t y = ln (\frac{x}{2}), at x = 4