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

The derivative of (2x-1^{-2}) is -4/((2x-1)^3)

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

The first derivative of (2x-1^{-2}) is -4/((2x-1)^3)

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

- \frac{4}{( 2 x - 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{( 2 x - 1 ) ^{3}} \cdot 2 : - \frac{4}{( 2 x - 1 ) ^{3}}

= - \frac{4}{( 2 x - 1 ) ^{3}}

What is the derivative of (2x-1^{-2}) ?
The derivative of (2x-1^{-2}) is -4/((2x-1)^3)
What is the first derivative of (2x-1^{-2}) ?
The first derivative of (2x-1^{-2}) is -4/((2x-1)^3)