What is the derivative of 1/(t^2-1) ?

The derivative of 1/(t^2-1) is -(2t)/((t^2-1)^2)

What is the first derivative of 1/(t^2-1) ?

The first derivative of 1/(t^2-1) is -(2t)/((t^2-1)^2)

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derivative of

\frac{1}{t ^{2} - 1}

- \frac{2 t}{( t ^{2} - 1 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{2 t}{( t ^{2} - 1 ) ^{2}}

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What is the derivative of 1/(t^2-1) ?
The derivative of 1/(t^2-1) is -(2t)/((t^2-1)^2)
What is the first derivative of 1/(t^2-1) ?
The first derivative of 1/(t^2-1) is -(2t)/((t^2-1)^2)