derivative of 3x^4-4x^3-12x^2+1

Lösung

\frac{d}{d x} (3 x^{4} - 4 x^{3} - 12 x^{2} + 1)

12 x^{3} - 12 x^{2} - 24 x

Schritte zur Lösung

\frac{d}{d x} (3 x^{4} - 4 x^{3} - 12 x^{2} + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (12 x^{2}) = 24 x

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

= 12 x^{3} - 12 x^{2} - 24 x + 0

Vereinfache

= 12 x^{3} - 12 x^{2} - 24 x

\int \frac{x ^{2} + 4 x + 10}{x ^{3} + 2 x ^{2} + 5 x} d x

\frac{d}{d x} (ln (x (1 - x)))

d er i v a t i v e ln (X^{\frac{1}{2}})

\int \frac{6}{( x + 1 ) ^{2}} d x

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