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Homework Help: Differentiation of an exponential function

  1. Jul 17, 2006 #1
    I have a problem involving natural logs which has got me confused, even though it appears simple.
    The problem: Find the exact coordinates of the point on [tex]y = e^x[/tex] where the gradient is 2.
    From previous experience, I know that differentiation is required, but because of the e I am not sure on how to go about this. After the differentiation I think I can manage to complete it.
  2. jcsd
  3. Jul 17, 2006 #2
    Well what is the derivative of [tex]y = e^x[/tex]?
  4. Jul 17, 2006 #3
    if you don't know it you can find out using the given that d/dx ln x = 1/x and then calculate d/dx ln [tex]e^x[/tex] using the chain rule
  5. Jul 17, 2006 #4
    If you know how to do this kind of problem then all you need is the derivative of e^x which is just e^x. Just do this problem as you would do if "y" was any other function, for example a polynomial.
  6. Jul 17, 2006 #5
    thanks for the help, however i am still unsure on how to approach this problem
  7. Jul 17, 2006 #6
    the derivative is the gradient, so the following must be solved:

    [tex]\frac {dy} {dx}\ = 2[/tex]

    This will give you the x-coordinate.
    Last edited: Jul 17, 2006
  8. Jul 17, 2006 #7


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    You "approach" this problem by differentiating ex! What is the derivative of ex? (It's the world's easiest derivative!)
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