# Constant Variables?

1. Sep 14, 2008

### azure kitsune

Once I was in my calculus class and I had to demonstrate an optimization problem on the board. It was finding the maximum area of a triangle inside a circle with radius r. When I got to the part where I had to differentiate, I said something along the lines of, "the derivative of r*t with respect to t is r, because r is a constant." But when I think about it, r is not a constant, because it is a variable!

So now I am really confused about whether something is a constant or not. Am I correct in saying that r is a constant?

(Sorry if this is in the wrong forum. Even though I used an example from calculus, I'm not sure if this is entirely a calculus topic so I put it in the general section.)

2. Sep 14, 2008

### rbj

probably, it would be better to say "the derivative of f(t) = rt with respect to t is r, because r is not a function of t."

if r is not a function of t, it may as well be constant (as far as variations of t are concerned).

3. Sep 14, 2008

### disregardthat

azure, I had the very same misconception before. When you differentiate something with respect to any variable, other variables is seen as constants, as these does not depend on the variable you are differentiating with respect to.