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Beliebt Rechnen >

derivative f(x)=(x^2-4)(x+1)

Lösung

ableitung von

f (x) = (x^{2} - 4) (x + 1)

Lösung

3 x^{2} + 2 x - 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} - 4, g = x + 1

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

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

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

= 2 x (x + 1) + 1 \cdot (x^{2} - 4)

Vereinfache

2 x (x + 1) + 1 \cdot (x^{2} - 4) : 3 x^{2} + 2 x - 4

= 3 x^{2} + 2 x - 4

Graph

Beliebte Beispiele

fläche 4x,x^2-12

a re a 4 x, x^{2} - 12

t^2y^{''}+7ty^'+5y=0

t^{2} y^{^{''}} + 7 t y^{^{'}} + 5 y = 0

derivative of x^2-sqrt(x)+5

\frac{d}{d x} (x^{2} - x + 5)

integral from 1 to 4 of 1/(x^2)

\int_{1}^{4} \frac{1}{x ^{2}} d x

derivative 1/((1+x^2))

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