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}}

\int \frac{csc ( θ )}{csc ( θ ) - sin ( θ )} d θ

\int 5 e^{- 2 t} sin (t) d t

\int (x + 2)^{2} (2 - x)^{6} d x

x^{3} + 3 x^{2} - 9 x

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)