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Math Help - Quick (& Easy) Derivative Clarification

  1. #1
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    Smile Quick (& Easy) Derivative Clarification

    Hello and thanks in advance for your help.

    I'm studying how derivatives are reflected in the shape of a function's graph and am doing pretty well with it, but had one clarifying question.

    Am I right in saying that if my given function f(x) = e^2x + e^-x, then...

    f'(x) = e^2x - e^-x

    f''(x) = e^2x + e^-x ?

    I'm mostly looking to confirm that those are right, but I'd like to understand better why the derivative of e^-x = -e^-x while the derivative of e^x = e^x.

    Thanks for any explanations/corrections!
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  2. #2
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    They are incorrect

     y = e^{f(x)} \Rightarrow \frac{dy}{dx} = f'(x)e^{f(x)}

    e.g

     y = e^{3x} \Rightarrow \frac{dy}{dx} = 3e^{3x}
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  3. #3
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    Excellent! So the chain rule is what I was missing AND why the derivative of e^-x = -e^-x!

    Thank you sir.

    P.S. - Good quotation in your signature.
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