ok so let me try to figure something out. This is a part of a related rates problem. I have area equals s squared divided by two, times sin theta. Now that I have a relation to area and theta, I am supposed to differentiate. Do I only differentiate the parts I want to find the rate of? or do I have to differentiate the entire thing?

Question

kira_yamato · Answer

I think it depends... Did the question give you any information? Because I tend to assume that everything is changing, which can become very complicated.

chrisplusian · Answer

it started as an iscoseles triangle and they asked you to prove that the area equals (s^2/2) sin(theta). then the used that formula to differentiate to find the rate of change of the are when theta is pi/6. the problem is that they put$$da/dt=(s^2 / 2)\cos \theta (d \theta/dt)$$ and I don't understand why they didn't differentiate "s^2" by the way "s" are the legs of the triangle that are equal

anonymous · Answer

is the length s changing over time? or just the angle?  if the side length isnt changing, its a constant.

anonymous · Answer

Another way to think about it is that you could differentiate all the variables with respect to time.  You would need to use the product rule in this case.  However, ds/dt would be 0, and wipe out the piece that would be effected by s changing, giving you what you put above.

anonymous · Answer

If this is from the problem you posted the other day (the half cylinder tank of water draining) I posted a solution for it on the other thread. http://openstudy.com/users/eseidl#/updates/4f7db580e4b09f22231c2add by the way, your original solution you had from another source was incorrect. the triangle is not an isosceles either.

chrisplusian · Answer

joemath314159...... can you explain a little more in depth how the ds/dt sould be zero and leave that part? I think that is what I am looking for.