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

The derivative of (2x^{-1}^2) is -8/(x^3)

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

The first derivative of (2x^{-1}^2) is -8/(x^3)

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

- \frac{8}{x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot 2 x^{- 1} (- \frac{2}{x ^{2}}) : - \frac{8}{x ^{3}}

= - \frac{8}{x ^{3}}

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

4 e^{\frac{2 t}{3}}

x \to 0 lim (\frac{6 sin ( 3 x )}{x})

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

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

What is the derivative of (2x^{-1}^2) ?
The derivative of (2x^{-1}^2) is -8/(x^3)
What is the first derivative of (2x^{-1}^2) ?
The first derivative of (2x^{-1}^2) is -8/(x^3)