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Beliebt Rechnen >

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

Lösung

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

Lösung

4 x^{3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 4 x^{3}

Graph

Beliebte Beispiele

derivative of 100xe^{-0.5x}

\frac{d}{d x} (100 x e^{- 0.5 x})

d/(dt)(e^{t/2})

\frac{d}{d t} (e^{\frac{t}{2}})

integral of 1/(x^2+3x)

\int \frac{1}{x ^{2} + 3 x} d x

integral of x*cos(npix)

\int x \cdot cos (nπ x) d x

(dy)/(dt)+20y=24

\frac{d y}{d t} + 20 y = 24