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Differentiating exponential

  1. Jun 21, 2011 #1
    Differentiate the following:

    u = 2 (x-t2 / 3)et/3

    Here is my attempt

    I have to find du/dx and du/dt

    du/dx = 2 (x-t2 / 3)et/3

    du/dt = -4t/9 (x-t2 / 3)et/3
     
  2. jcsd
  3. Jun 21, 2011 #2
    It would help if you wrote u as 2xet/3 - (2/3)t2et/3. Since u is a function of both t and x, you will have to use the chain rule in your derivatives.

    For example, if v = 3m2, then dv/dx = d/dx (3m2) = d/dm (3m2) (dm/dx) = 6m dm/dx.
     
  4. Jun 21, 2011 #3
    Ok so from what you have said:

    u = 2xet/3 - 2/3 t2et/3

    du/dx = 2/ e t/3

    du/dt = 2/3 xe t/3 - 4/9 t e t/3
     
  5. Jun 21, 2011 #4
    Ok du/dx
    There are errors in du/dt
     
  6. Jun 21, 2011 #5
    Ah yes I need to adopt the product rule on:

    -2/3 t2 e t/3
     
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