Couple quick derivative problems

[boscord]

If you could post solutions as to the answers and how you got them that would be MUCH! appreciated.

1. dy/dx of y = (3x^2 + 1) / (2x^2 -1)

2. dP/dv of P = (AB/V^2) - (C/V)

3. What is the formula for the instantaneous rate of change at [ t, f(t) ] ?

Thanks a bunch guys!

[plenderj]

The first two questions you need to use the "Quotient Rule" for finding the derivitave.
And for instantaneous rate of change of speed if I remember correctly, its a limit.

Lim (t) as t approaches 0, of v/t

[jemidiah]

As plenderj said, you need the quotient rule for the first one which is: (vdu - udv)/v² (my calc teacher has us remember it with this saying: low d-high minus high d-low over low-low in u/v )

The second one requires either the definition for finding the derivative (lim as h approaches 0 of (f(x + h) - f(x)) / h) or doing the limit as x approaches c (whatever you're finding) of f(x) which happens to be the exact same thing as derivative. You can also use the power rule to find the derivative (assuming you have the equation) and plug in c (as noted above).