## oio 3 years ago Hi! This question deals with derivatives Ok, here it is: The quantity demanded per month, y, of USEM tablets is related to the average price unit, p(t) (in dollars), of tablets by the equation y=f(p(t))= 10 * sqrt(810,000-[p(t)]^2) It is estimated that 3 months from now, the average price of the tablet will be given by p(t)= [400/(1+sqrt(t))] +500 (t is less than or equal to 60 and more than or equal to 0) I know I should use the Product and The Chain Rule, but I'm not sure how to apply it! Thank you in advance. I just need to find the derivative! I would really love an exp

1. saifoo.khan

@dpaInc

2. oio

$y=f(p(t))10\sqrt{810000-\left[ p \left( t \right) \right]^{2}}$ $p(t)=\frac{ 400 }{ 1+\sqrt{t} }+500$ I hope this is more helpful :(

I don't understand what the question wants. Two equations and that's it?

4. oio

oh whooop! AUGGHH! i forgot the rest hang on :) Find the rate at which the quantity of tablets deamnded per month will be changing 16 months from now!

5. oio

Thanks guys for helping me! :)

6. oio

Thank you for replying at the moment

LOL sorry. You might notice that $f(p(t))' = f'(p(t))* p'(t)$ And you have both. Now, for p(t), $p'(t)=400(1+\sqrt t)^-1 +500$ To use the chain rule, you can let u =(1+\sqrt t)^-1

p′(t)=(400(1+t√)−1+500)' sorry mistype

9. oio

thank you but...im still kind of confused... :( I really get confused when I derive f(p(t)) itself

yup, you might want to let it as u before starting...

11. oio

uhm thanks :)