What is the derivative of 1/(x^3-2x) ?

The derivative of 1/(x^3-2x) is -(3x^2-2)/((x^3-2x)^2)

What is the first derivative of 1/(x^3-2x) ?

The first derivative of 1/(x^3-2x) is -(3x^2-2)/((x^3-2x)^2)

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\frac{d}{d x} (\frac{1}{x ^{3} - 2 x})

- \frac{3 x ^{2} - 2}{( x ^{3} - 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{3} - 2 x})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{3} - 2 x)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{3} - 2 x ) ^{2}} \frac{d}{d x} (x^{3} - 2 x)

= - \frac{1}{( x ^{3} - 2 x ) ^{2}} \frac{d}{d x} (x^{3} - 2 x)

\frac{d}{d x} (x^{3} - 2 x) = 3 x^{2} - 2

= - \frac{1}{( x ^{3} - 2 x ) ^{2}} (3 x^{2} - 2)

Simplify

- \frac{1}{( x ^{3} - 2 x ) ^{2}} (3 x^{2} - 2) : - \frac{3 x ^{2} - 2}{( x ^{3} - 2 x ) ^{2}}

= - \frac{3 x ^{2} - 2}{( x ^{3} - 2 x ) ^{2}}

n \to \infty lim (- 1^{n})

\int_{0}^{π} 4 sin (x) + sin (4 x) d x

\frac{\partial}{\partial y} (1 - \frac{3}{x} + y)

x \to 0 lim (\frac{x ^{3} - 8}{x - 2})

\int e^{x} + 20 (1 + x^{2})^{- 1} d x

What is the derivative of 1/(x^3-2x) ?
The derivative of 1/(x^3-2x) is -(3x^2-2)/((x^3-2x)^2)
What is the first derivative of 1/(x^3-2x) ?
The first derivative of 1/(x^3-2x) is -(3x^2-2)/((x^3-2x)^2)