Other Random Math Help Prz

[Keno]

So I have an equation for total surplus and I need to find the derivative of this equation with respect to a variable that isn't in the equation. I'm pretty sure the whole damn point of this is to use the implicit function theorem, but in order for that to work I need to use real variables. Does anyone know how to use the IFT on something like this? If it helps, here is the exact problem.

Find dTS(j)/dt (t=tariff) : reads find the derivative of total surplus of the japanese market with respect to the tariff in the canadian market.

TS(j)=(1/2)*(qj^2) : reads total surplus of the japanese market is equal to one half multiplied by the quantity of units sold in the japanese market, squared.

I also have two other total surplus equations to use with the IFT. One has the tariff in the equation. I'm just not sure how to set up the IFT for this. Anyone know?

[Turambar]

Why isn't the answer just qj?

Edit #1:
Erg please ignore that. I just realized what a silly statement it was.

Anyways, it seems like you're missing an equation somewhere. dy/dt when you're only given y(x) can't be solved IIRC without some other equation x(t). That said, it's been about 8 years since I took calculus, so I could be forgetting something.

Edit #2:
Is that qj a constant "q" mulitiplied by a variable "j", or is it just a variable "qj"? From the way you use TS(j), it appears to be the former, but the description "one half multiplied by the quantity of units sold in the japanese market, squared" makes it sound like the latter is true.