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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} - 2) = 4 x

= - \frac{1}{( 2 x ^{2} - 2 ) ^{2}} \cdot 4 x

Simplify

- \frac{1}{( 2 x ^{2} - 2 ) ^{2}} \cdot 4 x : - \frac{x}{( x ^{2} - 1 ) ^{2}}

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

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