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Derivatives Problem (Calculus I)

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data
    find d/dt for a rectangle.


    2. Relevant equations
    A=bh
    product rule for derivatives (the first times the derivative of the second plus the second times the derivative of the first)
    Chain rule for derivatives

    3. The attempt at a solution
    If b is a constant, then I know that dA/dh = b (this was the previous problem in which I could solve)
    my issue with the current problem is that this variable t that I'm supposed to take the derivative with respect to is not in the problem- so how would I go about doing this?

    My attempt:
    d/dt (A=bh)
    dA/dt = bh
    dA/dt = (b(dA/dh)) + (h(dA/db))
    My only problem with this solution is that I think there should be a d(b or h)/dt on the right side of the equation because of the chain rule

    could someone please explain where/why the variable t comes in and what the correct answer is? Thank you!!
     
  2. jcsd
  3. Nov 7, 2012 #2

    micromass

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    I have no clue what this means. Can you quote the full problem as it appears in your book?
     
  4. Nov 7, 2012 #3
    that's my problem too... that IS the quote!

    "Find d/dt for a rectangle" and then the formula given is A=bh
    so find d/dt for A=bh
     
  5. Nov 7, 2012 #4

    micromass

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    Well, that makes no sense. I advice asking your teacher for more explanations.
     
  6. Nov 7, 2012 #5
    On a previous problem:
    Find d/dt for a square

    and the answer was:
    d/dt (A=s2)

    dA/dt = 2s (ds/dt)

    perhaps you understand this one? (I don't)
    well i know the derivative of s2 = 2s. so we've taken the derivative of A with respect to t... so perhaps multiplying 2s by ds/dt is part of the chain rule or something... I don't really know where ds/dt came from
     
  7. Nov 7, 2012 #6

    SammyS

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    Assume that b and h are both functions of time.

    There should be no derivatives of A on the right hand side of the following:

    dA/dt = (b(dA/dh)) + (h(dA/db))

    Use the product rule to find [itex]\displaystyle \frac{d}{dt}(b\,h)\ .[/itex
     
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