derivative of 4x^3-5x^2+4x-1

Lösung

\frac{d}{d x} (4 x^{3} - 5 x^{2} + 4 x - 1)

12 x^{2} - 10 x + 4

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} - 5 x^{2} + 4 x - 1)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (4 x) - \frac{d}{d x} (1)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (5 x^{2}) = 10 x

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

\frac{d}{d x} (1) = 0

= 12 x^{2} - 10 x + 4 - 0

Vereinfache

= 12 x^{2} - 10 x + 4

\int_{2}^{4} x e^{\frac{x}{2}} d x

d er i v a t i v e f (x) = \frac{1}{2 x - 1}

\int \frac{28}{28 + e ^{x}} d x

x \to 3 + lim (6 + x)

t an g e n t y = \frac{6}{x ^{2}}, (1, 6)