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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derivative of

(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)