Calculating Water Drainage Rate in a Tank Using Torricelli's Law

[morphine]

Homework Statement

If a tank holds 5,000 gallons of water which drains from the bottom of the tank
in 40 minutes, then Torricelli's Law gives the volume V of water reminaing in the
tank after t minutes as
V = 5000(1 - t / 40)², 0 <= t <= 40. The rate at which water is
draining from the tank after 10 minutes, in gal/min, is

Homework Equations

The Attempt at a Solution

I figure I'll just find f'(t).
[5000 lim _{h-> 0} (1 - (t+h)/40)²] - [5000 lim _h->0 (1 - t/40)²]

But now I'm stuck. I believe I have to use the power rule but don't see how to implement it.

 

[Mark44]

If you know some differentiation rules, such as the power rule you mentioned, that would be easier than using the definition of the derivative. For your particular function, the sum rule and constant multiple rule would be useful.

Also, don't call your derivative f'(t). Instead call it V'(t), which is the time rate of change of volume.

Finally, when you get V'(t), what are you going to do with it? Think about what this problem is asking for.