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Beliebt Rechnen >

derivative of 1/(x^2-2)

Lösung

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

Lösung

- \frac{2 x}{( x ^{2} - 2 ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of x^2+(128000/x)

\frac{d}{d x} (x^{2} + \frac{128000}{x})

fläche y=4-x^2,y=x^2-4x-2

a re a y = 4 - x^{2}, y = x^{2} - 4 x - 2

sum from n=2 to infinity of (3^n)/(10^n)

n = 2 \sum \infty \frac{3 ^{n}}{1 0 ^{n}}

taylor 1/(1+sin(pi*x))

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derivative of 1/(\sqrt[3]{(6x^2+5^2)})

\frac{d}{d x} \frac{1}{3 ( 6 x ^{2} + 5 ) ^{2}}