en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(ds)(1/(s^2-1))

Solution

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

Solution

- \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}}

Popular Examples

integral of (csc(θ))/(csc(θ)-sin(θ))

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

integral of 5e^{-2t}sin(t)

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

integral of (x+2)^2(2-x)^6

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

tangent of x^3+3x^2-9x tangent of

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

integral of \sqrt[6]{cot(x)}csc^2(x)

Frequently Asked Questions (FAQ)

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)