derivative of (x-2^3+x)

Lösung

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

3 x^{2} - 12 x + 13

Schritte zur Lösung

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

Vereinfache

(x - 2)^{3} + x : x^{3} - 6 x^{2} + 13 x - 8

= \frac{d}{d x} (x^{3} - 6 x^{2} + 13 x - 8)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (13 x) - \frac{d}{d x} (8)

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

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (13 x) = 13

\frac{d}{d x} (8) = 0

= 3 x^{2} - 12 x + 13 - 0

Vereinfache

= 3 x^{2} - 12 x + 13

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

x \to + 5 lim (5 - x)

\int_{2}^{3} \frac{1}{x ^{\frac{2}{3}}} d x

\int 3 x^{2} 3 (5 x^{3} + 4)^{5} d x

t an g e n t 2 3 x, at x = 1