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How do you decide what is dy/dt, or dx/dt

  1. Feb 14, 2016 #1
    1. The problem statement, all variables and given/known data
    if y=2t+3 and x=t^2, find dy/dx

    2. Relevant equations
    dy=dy/dt*dt/dx

    3. The attempt at a solution
    dy/dt=2
    dx/dt=2t
    therefore dy/dx=1/t
    what I don't understand is how the dy/dt etc. is found when attempting this problem
     
  2. jcsd
  3. Feb 14, 2016 #2

    SteamKing

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    Well, look at each equation in turn

    The first equation is y = 2t + 3. What is dy/dt?

    If this equation were written y = 2x + 3, would you have any problem finding dy/dx?

    The second equation is x = t2

    What if you wanted to find dy/dx for y = x2 ?

    The rules of differentiation that you are supposed to learn are written around finding the change in the dependent variable with respect to the change in the independent variable. Since y is usually the dependent variable and x is the independent variable, the rules all state dy/dx = whatever.

    For example, if y = xn, then dy/dx = n ⋅ xn-1
     
  4. Feb 14, 2016 #3

    andrewkirk

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    Do you know how to differentiate the formula 2t+3 with respect to t?
     
  5. Feb 14, 2016 #4
    i understand differentiation in that you could find the derivative by going (2*1)t^(1-1) =2 i'm not clear on how it relates to dy/dt and combining it with dx/dt
     
  6. Feb 14, 2016 #5
    i suppose what im asking would be; what does dy/dt mean? I can't wrap my head around the explanation in my textbook and im looking for a dumbed down version
     
  7. Feb 14, 2016 #6

    andrewkirk

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    It is the rate of increase of y as t increases. Loosely put, it is the size of the tiny increase in y that would arise from making a tiny increase to t and putting that in the formula for y. If you do a line graph of y on the vertical axis against t on the horizontal axis it is the slope (gradient) of the line.
     
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