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

The derivative of (1+q^{-1})^2 is -(2(q+1))/(q^3)

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

The first derivative of (1+q^{-1})^2 is -(2(q+1))/(q^3)

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derivative of

(1 + q^{- 1})^{2}

- \frac{2 ( q + 1 )}{q ^{3}}

Solution steps

\frac{d}{d q} ((1 + q^{- 1})^{2})

Apply the chain rule:

2 (1 + q^{- 1}) \frac{d}{d q} (1 + q^{- 1})

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

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

= 2 (1 + q^{- 1}) (- \frac{1}{q ^{2}})

Simplify

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

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

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