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Thread: Implicit differentiation

  1. #1 Implicit differentiation 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    How would one solve this;


    where y is a function of x??

    would appreciate any help.


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  3. #2  
    Forum Masters Degree organic god's Avatar
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    i see 1 equation with 2 unknowns.

    what do we have to solve?


    everything is mathematical.
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  4. #3  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    oops my bad, its alright i know how to solve it now. You are supposed to get
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  5. #4  
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    Quote Originally Posted by Heinsbergrelatz
    oops my bad, its alright i know how to solve it now. You are supposed to get

    Product rule or chain rule, one or the other, look em up I forget them.

    Maybe both who knows?
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  6. #5  
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    so x= y sin y^2

    so for x-siny^2 dx/dy = 2ycos y^2

    So dx/dy = sin y^2 + y2y cos y^2


    = sin y^2 + 2y^2 cos y^2


    thus dy/dy=

    ................ 1
    = ---------------------

    sin y^2 + 2y^2 cos y^2


    Is that the answer?
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  7. #6  
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    Quote Originally Posted by smokey
    so x= y sin y^2

    so for x-siny^2 dx/dy = 2ycos y^2

    So dx/dy = sin y^2 + y2y cos y^2


    = sin y^2 + 2y^2 cos y^2


    thus dy/dy=

    ................ 1
    = ---------------------

    sin y^2 + 2y^2 cos y^2


    Is that the answer?
    no.

    The answer is simply
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  8. #7  
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    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by smokey
    so x= y sin y^2

    so for x-siny^2 dx/dy = 2ycos y^2

    So dx/dy = sin y^2 + y2y cos y^2


    = sin y^2 + 2y^2 cos y^2


    thus dy/dy=

    ................ 1
    = ---------------------

    sin y^2 + 2y^2 cos y^2


    Is that the answer?
    no.

    The answer is simply
    That is dx/dy I believe not dy/dx
    Bit of a trick really.
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  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    we have to express only in terms of y and x, sorry for not noting all the details. so its supposed to be;









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  10. #9  
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    That looks a bit ropey to me.
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  11. #10  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    That looks a bit ropey to me.

    well that is the only possible case when expressing the derivative in terms of x and y, got any other alternatives if you say its "ropey"?
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  12. #11  
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    Quote Originally Posted by smokey
    That looks a bit ropey to me.
    He's absolutely correct.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  13. #12  
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    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by smokey
    That looks a bit ropey to me.
    He's absolutely correct.

    Who me?


    Yes he is correct, I did not notice what he did initially but looking again
    I see he substituted back in the initial equation into the result to get a
    simpler answer,
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