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Math Help - derivatives

  1. #1
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    derivatives

    Can someone help me out with this questions? I am completely lost.

    A) If y=ln{x+(x^2-a^2)}, evaluate dy/dx, expressing your answer in its simplest form.

    Show that (x^2 - a^2) d^(2)y/dx^2 +x(dy/dx)=0
    Last edited by mr fantastic; November 28th 2009 at 01:06 PM. Reason: Changed font size to default so that the question could actually be read without using a microscope.
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  2. #2
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    Quote Originally Posted by sderosa518 View Post
    Can someone help me out with this questions? I am completely lost.
    A) If y=ln{x+(x^2-a^2)}, evaluate dy/dx, expressing your answer in its simplest form. Show that
    (x^2 - a^2) d^(2)y/dx^2 +x(dy/dx)=0
    check your original log function and the conclusion you're supposed to reach ... as you've written it, it doesn't work.
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    I copy the problem down right. Is it possible for you to write out the problem that you are reading or the equation, but its 100% correct
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    Quote Originally Posted by sderosa518 View Post
    I copy the problem down right. Is it possible for you to write out the problem that you are reading or the equation, but its 100% correct
    y = \ln\left[x + (x^2-a^2)\right]

    \frac{dy}{dx} = \frac{2x+1}{x+(x^2-a^2)}

    \frac{d^2y}{dx^2} = \frac{2[x+(x^2-a^2)] - (2x+1)^2}{[x + (x^2-a^2)]^2} = -\frac{2x^2+2x+2a^2+1}{[x+(x^2-a^2)]^2}


    x \cdot \frac{dy}{dx} = \frac{x(2x+1)}{x+(x^2-a^2)}

    (x^2-a^2) \cdot \frac{d^2y}{dx^2} = \frac{(a^2-x^2)(2x^2+2x+2a^2+1)}{[x+(x^2-a^2)]^2}

    ... now, see if you can get the last two expressions to add up to 0.
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    With all do with respect, can you show the final answer. As you were saying, the problem is written down incorrect. R u trying to tell me that there is no solution, but if there is can you finish for me. i would appreciate it!!!
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    Quote Originally Posted by sderosa518 View Post
    With all do with respect, can you show the final answer. As you were saying, the problem is written down incorrect. R u trying to tell me that there is no solution, but if there is can you finish for me. i would appreciate it!!!
    I am telling you that this statement ...

    Show that
    (x^2 - a^2) d^(2)y/dx^2 +x(dy/dx)=0
    does not work.
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  7. #7
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    Thats part of my homework assignment. Its in my calculus book.
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  8. #8
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    Quote Originally Posted by sderosa518 View Post
    Thats part of my homework assignment. Its in my calculus book.
    Look, there's a problem with the question as posted. This has been said several times now. Sorting out this problem is not our job. It's your teacher's job. So speak to your teacher.
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  9. #9
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    Lets try this. this is exactly how the problem is written.

    Check attachment..

    Let me know if its better, if it doesnt work, then I will go to my professor.

    Thank You
    Attached Files Attached Files
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  10. #10
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    Quote Originally Posted by sderosa518 View Post
    Lets try this. this is exactly how the problem is written.

    Check attachment..

    Let me know if its better, if it doesnt work, then I will go to my professor.

    Thank You
    nothing 's changed ... get your professor to show you how the last statement is true.

    I eagerly await to see his/her complete solution.
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  11. #11
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    Indeed!! When he shows me the answer, ill get back to you as soon as possible.
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  12. #12
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    Skeeter your right!!!! It cant be solve. Doesnt equal zero. the professor tried to solve to zero, its not possible. My professor is wrong. Anyway thank you for you help.
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  13. #13
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    Skeeter,

    We found out what was wrong with the solution. The person who type up the test left an exponent. Thhhhhhh

    y=ln{x+(x^2-a^2)^(1/2)},
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