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Math Help - Elimination of Arbitrary Constants 3

  1. #1
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    Elimination of Arbitrary Constants 3

    How do I eliminate the arbitrary constant A from the function: y = Ae^(3x)?

    Here is my attempt:

    y = Ae^(3x)

    dy/dx = (how do I differentiate Ae^(3x) ) ??
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  2. #2
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    Quote Originally Posted by sparky View Post
    How do I eliminate the arbitrary constant A from the function: y = Ae^(3x)?

    Here is my attempt:

    y = Ae^(3x)

    dy/dx = (how do I differentiate Ae^(3x) ) ??
    What is the exact question you are doing?

    \displaystyle\frac{dy}{dx}=3Ae^{3x}=A_1e^{3x}
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  3. #3
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    e^x is the world's easiest function to differentiate! Its derivative is just itself, e^x. To differentiate e^{3x}, use the chain rule to get the derivative dwsmith did.

    To get an equation that does not involve the constant A, divide the derivative of y by y:
    \frac{dy}{dx}= \frac{3Ae^{3x}}{Ae^{3x}}= 3.
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