derivative of (x+1*(x^2-1))

Lösung

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

3 x^{2} + 2 x - 1

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 1, g = x^{2} - 1

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

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

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

= 1 \cdot (x^{2} - 1) + 2 x (x + 1)

Vereinfache

1 \cdot (x^{2} - 1) + 2 x (x + 1) : 3 x^{2} + 2 x - 1

= 3 x^{2} + 2 x - 1

d er i v a t i v e \frac{x ^{2} - 3}{x - 2}

d er i v a t i v e y = (5 x^{2} - 6 x)^{- 2}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 6} d x

\int x^{2} e^{x} sin (x) d x

\frac{\partial}{\partial x} (x y + x e^{\frac{1}{y}})