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

Lösung

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

3 x^{2} + 6 x

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

= 3 x^{2} + 6 x - 0

Vereinfache

= 3 x^{2} + 6 x

θ \to + 0 lim (\frac{tan ( 2 θ )}{θ})

x \to 3 + lim (\frac{x - 3}{x - 2 - 4 - x})

n = 1 \sum \infty i^{2 n}

n = 2 \sum \infty n (\frac{3}{4})^{n}

x \to 1 lim (\frac{x}{x - 1})