find  `y'`  when  `y=(t^2+8t)/(3t)`  without using the quotient rule.

Expert Answers
lfryerda eNotes educator| Certified Educator

To find the derivative of this function, we first want to simplify it, then we can take the derivative.

Notice that when `t ne 0` , 

`y={t^2+8t}/{3t}`   divide numerator and denominator by `t`


now we can take the derivative.  In this case, we just have a power rule for the first term, and the second term is a constant, so its derivative is zero.

`y' = 1/3`

Without using the quotient rule, the derivative is `y'=1/3` .