Differentiate each function by applying the basic rules of differentiation
`(3t^(2)+7)/(t^(2)-1)`

Explanation

To differentiate the function \( y = \frac{3t^2 + 7}{t^2 - 1} \), we will apply the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dt} \) is given by:

\[ \frac{dy}{dt} = \frac{v \frac{du}{dt} - u \frac{dv}{dt}}{v^2} \]

where \( u = 3t^2 + 7 \) and \( v = t^2 - 1 \).

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