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Chain Rule

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Finda dw/dt
    w=3xy/x²-y²
    x=t3
    y=e2t

    2. Relevant equations
    w=(3t3e2t)/(t6-e4t)


    3. The attempt at a solution
    Well,is there anothe way to solve this, instead of dw/dt; like dw/dx * dw/dt + dw/dy * dy/dt ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 11, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sure. You could just the chain rule as well. You should get the same answer both ways. Just substituting like you did looks to be a little easier.
     
  4. Mar 13, 2009 #3
    Chain Rule Exponential and logarithmic

    f(x) = ln [ e^ln(x+1) ]
    f' = ?
     
  5. Mar 13, 2009 #4

    Mark44

    Staff: Mentor

    Simplify it a bit first to make your differentiation easier. What is ln(e^whatever)?
     
  6. Mar 13, 2009 #5
    f(x) = ln { e^[ln(x+1)] }

    well, i have this answer, but i dont understand
    ln [ e^ln(x+1) ] = ln(x+1)

    f'(x) = 1/(e^ln(x+1)) * e^ln(x+1) * 1/(x+1) = 1/(x+1)
     
  7. Mar 13, 2009 #6

    Mark44

    Staff: Mentor

    The ln and exp functions are inverses of one another, so for any real number u, ln(eu) = u. This means that you can simplify your function before taking its derivative. Then, what you end up differentiating is much simpler.
     
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