What is the derivative of (s^2+a)^{-2} ?

The derivative of (s^2+a)^{-2} is -(4s)/((s^2+a)^3)

What is the first derivative of (s^2+a)^{-2} ?

The first derivative of (s^2+a)^{-2} is -(4s)/((s^2+a)^3)

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derivative of

(s^{2} + a)^{- 2}

- \frac{4 s}{( s ^{2} + a ) ^{3}}

Solution steps

\frac{d}{d s} ((s^{2} + a)^{- 2})

Apply the chain rule:

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

= - \frac{2}{( s ^{2} + a ) ^{3}} \frac{d}{d s} (s^{2} + a)

\frac{d}{d s} (s^{2} + a) = 2 s

= - \frac{2}{( s ^{2} + a ) ^{3}} \cdot 2 s

Simplify

- \frac{2}{( s ^{2} + a ) ^{3}} \cdot 2 s : - \frac{4 s}{( s ^{2} + a ) ^{3}}

= - \frac{4 s}{( s ^{2} + a ) ^{3}}

What is the derivative of (s^2+a)^{-2} ?
The derivative of (s^2+a)^{-2} is -(4s)/((s^2+a)^3)
What is the first derivative of (s^2+a)^{-2} ?
The first derivative of (s^2+a)^{-2} is -(4s)/((s^2+a)^3)