What is the derivative of 1/(x^2-2) ?

The derivative of 1/(x^2-2) is -(2x)/((x^2-2)^2)

What is the first derivative of 1/(x^2-2) ?

The first derivative of 1/(x^2-2) is -(2x)/((x^2-2)^2)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \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

Simplify

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

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

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

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

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

\frac{1}{1 + sin ( π \cdot x )}

What is the derivative of 1/(x^2-2) ?
The derivative of 1/(x^2-2) is -(2x)/((x^2-2)^2)
What is the first derivative of 1/(x^2-2) ?
The first derivative of 1/(x^2-2) is -(2x)/((x^2-2)^2)