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Math Help - Basic partial derivative question

  1. #1
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    Question Basic partial derivative question

    I am reviewing some concepts and I do not remember the proper way solve this problem.
    I need to differentiate f with respect to x and with respect to y (partial derivatives) for:
    f(x,y) = ln(x^5+xy+(y^3)(e^x))
    My guess is that f with respect to x is:

    (5x^4+y+(y^3)(e^x))((1/ (x^5+xy+(y^3)(e^x)))
    But I am pretty sure that my guess is not correct. Can anyone help me with this, please?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by alekb View Post
    I am reviewing some concepts and I do not remember the proper way solve this problem.
    I need to differentiate f with respect to x and with respect to y (partial derivatives) for:
    f(x,y) = ln(x^5+xy+(y^3)(e^x))
    My guess is that f with respect to x is:

    (5x^4+y+(y^3)(e^x))((1/ (x^5+xy+(y^3)(e^x)))
    But I am pretty sure that my guess is not correct. Can anyone help me with this, please?
    You tell us. \frac{\partial}{\partial x}f(x,y) is just like considering f(x,y) as a function of x and treating y as constant.
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  3. #3
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    you can see the attachment for the answer

    the mistake you were making is for the implicit differentiation part


    for example IF you have to differentiate f(x) = xy



    then you use product rule = derivative of the first times the second + the derivative of the second times the first = 1y + y'x when you differentiate y then you get y'



    Second example f(x)= (x^3)(y^3) = 3(x^2)(y^3) + 3(y^2)y'(x^3)


    you can review implicit differentiation from youtube
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  4. #4
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    I thought that I did not need to add the y part of it while differentiating for x.

    I know that the derivative of ln(x) is 1/x, based on that assumption I solved ln(x^5+xy+(y^3)(e^x)) as 1/(x^5+xy+(y^3)(e^x)).

    My problem is that I do not know how to link the derivative of the part inside the brackets with the derivative of ln(x).

    Because I am treating y as a constant, I took the derivative of the part inside the brackets and connected it with the derivative of ln(x); however I do not know if I am supposed to do this:

    ((1/ (x^5+xy+(y^3)(e^x)))(5x^4+y+(y^3)(e^x))
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  5. #5
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    Sorry about the wrong information. I have not learned partial derivatives yet in Calculus. I just looked it up on Google and you are right about treating y as a constant. I thought you were talking about implicit differentiation. I am sorry for the misunderstanding.
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