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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Graph

Beliebte Beispiele

derivative of (2tan(x)/x)

\frac{d}{d x} (\frac{2 tan ( x )}{x})

sum from n=0 to infinity of 1/(5n+1)

n = 0 \sum \infty \frac{1}{5 n + 1}

tangent 2x^3-4x+6

t an g e n t 2 x^{3} - 4 x + 6

(\partial)/(\partial x)(5-3x+6y-2x^2y)

\frac{\partial}{\partial x} (5 - 3 x + 6 y - 2 x^{2} y)

steigung (1,6),(7,3)

s l o p e (1, 6), (7, 3)