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Thread: how to differentiate e^(x/y) with respect to 1) x and 2) y

  1. #1

    how to differentiate e^(x/y) with respect to 1) x and 2) y

    how to differentiate e^(x/y) with respect to
    1) x and
    2) y

  2. #2
    Elite Member
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    Quote Originally Posted by itsmusa7 View Post
    how to differentiate e^(x/y) with respect to
    1) x and
    2) y
    Start with

    [tex]\displaystyle f(x,y) = e^{\frac{x}{y}}[/tex]

    Now for (1) calculate [tex]\frac{df}{dx}[/tex], treating y as constant

    then for (2) calculate [tex]\frac{df}{dy}[/tex], treating x as constant

    Please share your work with us .

    If you are stuck at the beginning tell us and we'll start with the definitions.

    You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

    http://www.freemathhelp.com/forum/th...217#post322217
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3

    Re: how to differentiate e^(x/y) with respect to 1) x and 2) y

    Thank You sir for helping me, but I think I haven't got the help I needed. I needed the process of differentiating e^(x/y) with respect to 1) x and 2) y, especially " y ", because I know the process of differentiating it with respect to " x ", but never did it with respect to " y ". And I think I've posted my question in the wrong category. Sorry for that. I have read your forum rules " before posting " and I'll be careful in future. Thanks

  4. #4
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    Quote Originally Posted by itsmusa7 View Post
    Thank You sir for helping me, but I think I haven't got the help I needed. I needed the process of differentiating e^(x/y) with respect to 1) x and 2) y, especially " y ", because I know the process of differentiating it with respect to " x ", but never did it with respect to " y ". And I think I've posted my question in the wrong category. Sorry for that. I have read your forum rules " before posting " and I'll be careful in future. Thanks
    suppose you had:

    z = e^(a/x) ................ where 'a' is a constant

    can you calculate dz/dx?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  5. #5
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    What you need is the "chain rule": the derivative of [tex]e^{f(x)}[/tex] with respect to x is [tex]e^{f(x)}\frac{df}{dx}[/tex].

    Now, differentinating [tex]e^{x/y}[/tex] with respect to x, f(x)= x/y. What is the derivative of x/y with respect to x?

    Differentiating [tex]e^{x/y}[/tex] with respect to y, [tex]f(y)= x/y= xy^{-1}[/tex]. What is the derivative of [tex]xy^{-1}[/tex] with respect to y?

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