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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

4 x^{3} e^{- x}

\int cos^{3} (\frac{x}{5}) d x

f (x) = (x^{3} - 16 x)^{14}, (4, 0)

x \to 8 lim (5)

\int e^{- y} d y

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