# How do you differentiate #s=(t^2+1)/(1-t^2)#?

Use the quotient rule.

Now use algebra to simplify.

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To differentiate ( s = \frac{t^2 + 1}{1 - t^2} ), you can use the quotient rule of differentiation:

[ \frac{d}{dt} \left( \frac{u}{v} \right) = \frac{u'v - uv'}{v^2} ]

Where ( u = t^2 + 1 ) and ( v = 1 - t^2 ). Differentiate ( u ) and ( v ) with respect to ( t ):

[ u' = 2t ] [ v' = -2t ]

Now, substitute these into the quotient rule:

[ s' = \frac{(2t)(1 - t^2) - (t^2 + 1)(-2t)}{(1 - t^2)^2} ]

[ s' = \frac{2t - 2t^3 + 2t^3 + 2t}{(1 - t^2)^2} ]

[ s' = \frac{4t}{(1 - t^2)^2} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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