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Math Help - Some derivative questions

  1. #1
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    Some derivative questions

    I could use some help on the following derivative questions.....



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    -------

    ,


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    Quote Originally Posted by redraider717 View Post
    I could use some help on the following derivative questions.....



    ---------



    ----------



    -------

    ,


    ----------


    What help, specifically, do you need?

    The rule that is being tested here is
    \frac{d}{dx}e^x = e^x.

    For example, the first one is just the product rule:
    f(x) = (x + 3)e^x

    f^{\prime}(x) = 1 \cdot e^x + (x + 3)e^x = (x + 4)e^x

    -Dan
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  3. #3
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    It's e^-x

    I'm not sure what the derivative of e^-x is

    I'm also not sure what to do with 2e^x
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    Quote Originally Posted by redraider717 View Post
    It's e^-x

    I'm not sure what the derivative of e^-x is
    in general, \frac d{dx}e^{kx} = ke^{kx}

    here, k = -1

    I'm also not sure what to do with 2e^x
    recall that \frac d{dx}cf(x) = c \frac d{dx}f(x) where c is a constant.

    thus, \frac d{dx}2e^x = 2 \frac d{dx}e^x = 2e^x

    (basically this means, when deriving something with a constant coefficient, you can pretty much ignore the constant, find the derivative of the function, and then affix (multiply by) the constant again.
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  5. #5
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    Also on 3/x+3 wouldn't this be the answer....


    (3)'(x+3)-(x+3)'(3)/(x+3)^2

    (0)(x+3)-(1)(0)(3)/(x+3)^2

    0/(x+3)^2= undefined....
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    Quote Originally Posted by redraider717 View Post
    Also on 3/x+3 wouldn't this be the answer....


    (3)'(x+3)-(x+3)'(3)/(x+3)^2

    (0)(x+3)-(1)(0)(3)/(x+3)^2

    0/(x+3)^2= undefined....
    first of all \frac 0{(x + 3)^2} is not undefined.

    secondly, the derivative of x + 3 is 1, so you would end up with \frac {-3}{(x + 3)^2}
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  7. #7
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    I have another simple question.

    What's the derivative of

    3lnx?
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    Quote Originally Posted by redraider717 View Post
    I have another simple question.

    What's the derivative of

    3lnx?
    Quote Originally Posted by Jhevon View Post
    ... recall that \frac d{dx}cf(x) = c \frac d{dx}f(x) where c is a constant...
    what do you think?
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  9. #9
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    3(1/x)?
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    Quote Originally Posted by redraider717 View Post
    3(1/x)?
    correct. or we could say 3/x, same thing, but it looks nicer
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  11. #11
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    Also do you happen to use webwork or know how to type in

    cubed root of 3

    and is 1/e^x not 1/e^x?
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    Quote Originally Posted by redraider717 View Post
    Also do you happen to use webwork or know how to type in

    cubed root of 3
    i do not know how it is in webwork, but it is probably 3^(1/3) or something like that. i don't know if cubert(3) would work either. shouldn't there be some kind of tutorial for how to enter things into your webwork program?

    and is 1/e^x not 1/e^x?
    what?! you wrote the same thing twice, of course they are the same

    1/(e^x) = e^(-x) if that makes it any easier for you

    another common way to type e to some power is to type exp(some power)

    so 1/(e^x) = e^(-x) = exp(-x)
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  13. #13
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    Well the actual problem has e^-x in it but I knew that was 1/e^x and the derivative of e^x is e^x so I figured (1/e^x)' was 1/e^x
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    Quote Originally Posted by redraider717 View Post
    Well the actual problem has e^-x in it but I knew that was 1/e^x and the derivative of e^x is e^x so I figured (1/e^x)' was 1/e^x
    no, that is wrong. if you changed it to 1/(e^x) you would have to use the quotient rule.

    just use the rule i told you: \frac d{dx}e^{kx} = ke^{kx}

    here, k = -1
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