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Math Help - Derivative

  1. #1
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    Derivative

    Given:

    Q(x) =4x^2 + 20x + 25/ e^x


    Find Stationary Point and give its functional value.

    Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?
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  2. #2
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    Differentiating

    Hello ibrox
    Quote Originally Posted by ibrox View Post
    Given:
    Quote Originally Posted by ibrox View Post
    Q(x) =4x^2 + 20x + 25/ e^x


    Find Stationary Point and give its functional value.

    Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?
    The short answer to your question is that

    \frac{d}{dx}(e^x) = e^x

    But you'll need to write \frac{25}{e^x} as 25e^{-x}, whose derivative is -25 e^{-x}. But you'll still have some difficulty in finding where \frac{dQ}{dx}=0. It's not a straightforward equation to solve...

    Grandad
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  3. #3
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    Quote Originally Posted by ibrox View Post
    Given:

    Q(x) =4x^2 + 20x + 25/ e^x


    Find Stationary Point and give its functional value.

    Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?
    1. If f(x)=e^x then f'(x)=e^x

    2. Probably you mean:

    Q(x) =(4x^2 + 20x + 25) / e^x

    If so use the quotient rule:

    Q'(x)=\dfrac{e^x(8x+20) - (4x^2+20x+25)\cdot e^x}{e^{2x}}

    3. Factor out the e^x in the numerator and cancel. Afterwards collect like terms in the numerator. You'll get:

    Q'(x)=\dfrac{-4x^2-12x-5}{e^x}

    4. I'll leave all further examinations for you.
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  4. #4
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    Grandad:

    I actually looked up Euler's number on wikipedia and what I looked under the derivative is what you gave me, was unable to understand it.

    Earboth:

    Thanks a lot, I should be okay from here on out.

    Nice to get help from you guys, the math help centre on my university campus is useless.

    Ibrox
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