What is the d/(ds)(1/(s+2)) ?

The d/(ds)(1/(s+2)) is -1/((s+2)^2)

What is the first d/(ds)(1/(s+2)) ?

The first d/(ds)(1/(s+2)) is -1/((s+2)^2)

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\frac{d}{d s} (\frac{1}{s + 2})

- \frac{1}{( s + 2 ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{1}{s + 2})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d s} (s + 2) = 1

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

Simplify

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

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