derivative of 4x^3+3x^2-6x+1

Lösung

\frac{d}{d x} (4 x^{3} + 3 x^{2} - 6 x + 1)

12 x^{2} + 6 x - 6

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} + 3 x^{2} - 6 x + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (6 x) = 6

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

= 12 x^{2} + 6 x - 6 + 0

Vereinfache

= 12 x^{2} + 6 x - 6

x \to 0 + lim (\frac{4}{x ^{2} - x})

\frac{\partial}{\partial y} (y e^{x y} + y)

d er i v a t i v e x^{3} - 5 x^{2} + 13

\frac{d}{d x} (e^{s i n (x)})

\int e^{2 x} + x^{3} d x