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Math Help - derivatives of e functions

  1. #1
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    derivatives of e functions

    a little confused on this problem, any step by step help is appreciated.

    find the derivative and f`(0)

    f(x) = e^(x^2 + 2) / e^(x^2) + 1
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    Quote Originally Posted by JGaraffa View Post
    f(x) = e^(x^2 + 2) / e^(x^2) + 1
    Is it f(x) = \dfrac{e^{x^2 + 2}}{ e^{x^2+ 1}}, or f(x) = \dfrac{e^{x^2 + 2}}{ e^{x^2}+ 1}, or f(x) = \dfrac{e^{x^2 + 2}}{ e^{x^2}}+1? When posting a question, your priority must be on clarity.
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  3. #3
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    2nd one. sorry i don't really know how to use the symbols.
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  4. #4
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    Quote Originally Posted by JGaraffa View Post
    a little confused on this problem, any step by step help is appreciated.

    find the derivative and f`(0)

    f(x) = e^(x^2 + 2) / [e^(x^2) + 1]
    quotient rule ...

    \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \cdot u' - u \cdot v'}{v^2}

    f'(x) = \frac{(e^{x^2}+1)e^{x^2+2} \cdot 2x - e^{x^2+2} \cdot e^{x^2} \cdot 2x}{(e^{x^2}+1)^2}

    evaluate f'(0)
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  5. #5
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    Quote Originally Posted by JGaraffa View Post
    2nd one. sorry i don't really know how to use the symbols.
    If f(x) = \dfrac{e^{x^2 + 2}}{ e^{x^2}+ 1}, then, using the quotient rule, f'(x) = \dfrac{\left(e^{x^2}+ 1\right)\dfrac{d}{dx}\left(e^{x^2 + 2}\right)-\left(e^{x^2 + 2}\right)\dfrac{d}{dx}\left(e^{x^2}+ 1\right)}{\left(e^{x^2}+1\right)^2} . By the Chain Rule, \dfrac{d}{dx}\left(e^{x^2 + 2}\right) = 2xe^{x^2+2} and \dfrac{d}{dx}\left(e^{x^2}+ 1\right) = 2e^{x^2}. So f'(x) = \dfrac{\left(e^{x^2}+ 1\right)\left(2xe^{x^2+2}\right)-\left(e^{x^2 + 1}\right)\left(2e^{x^2}\right)}{\left(e^{x^2}+1\ri  ght)^2}. Simplifying this gives  f'(x)= \boxed{\dfrac{2e^{x^2+2}x}{\left(e^{x^2}+1\right)}- \dfrac{2e^{2 x^2+2}x}{(e^{x^2}+1)^2}}. To find f'(0), let x = 0.

    You can learn how to use the Latex from here.
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  6. #6
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    thanks for your help guys i really appreciate it. hopefully you're still around to check this and i won't have to post another thread for a simple question...

    when solving for f`(0) what is the correct order of operations for functions of e such as the one's above. for example, for e^(x^2) would i do 0^2 * e^x ? cause when i do that the answer comes out to zero, and online function calculators tell me the answer should come out to 2.

    same for e^(x^2 + 2)



    ugh sorry i'm still really bad at this latex stuff.
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