Compute the derivative of the given function in two different ways.

a) Use the Quotient Rule, $\displaystyle\left[\frac{f}{g}\right]' = \frac{g\cdot f' - f \cdot g'}{g^2}$. (Fill in each blank, then simplify.)

$f'(t) = \Big[\Big($ $\Big) \cdot \Big($ $\Big) - \Big($ $\Big) \cdot \Big($ $\Big)\Big] / \Big($ $\Big)$
= .

b) Use algebra first to simplify $f$, then differentiate without the Quotient Rule.

$f'(t) =$ .