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Math Help - differentiating implicitly....little help

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    differentiating implicitly....little help

    i understand the main concept of differentiating implicitly, however i cant seem to get this problem,

    sin(xy)=6x+7

    can someone please help me with this one...much thanks...

    mathaction
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaction View Post
    i understand the main concept of differentiating implicitly, however i cant seem to get this problem,

    sin(xy)=6x+7

    can someone please help me with this one...much thanks...

    mathaction
    you need the chain rule (coupled with the product rule) for the LHS. here goes:

    \sin (xy) = 6x + 7

    differentiating implicitly with respect to x, we get:

    \cos (xy) \cdot (y + x~y') = 6

    now solve for y'
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    Quote Originally Posted by Jhevon View Post
    you need the chain rule (coupled with the product rule) for the LHS. here goes:

    \sin (xy) = 6x + 7

    differentiating implicitly with respect to x, we get:

    \cos (xy) \cdot (y + x~y') = 6

    now solve for y'
    yeah when i was doing it for some reason i was putting dy/dx on the cos(xy), but this helped, i came up with...

    (6-ycos(xy))/(xcos(xy))
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaction View Post
    yeah when i was doing it for some reason i was putting dy/dx on the cos(xy), but this helped, i came up with...

    (6-ycos(xy))/(xcos(xy))
    that's correct
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    i have just one more, about implicity differentiation...for this problem...

    x^3 + 5x^2y + 2y^2 = 4y + 11

    the last answer i came up with was...

    (-3x^2-10xy)/(5x^2+4y-1)

    then it wanted the slope of the tangent line at (1,2), but when i plugged these in the answer was wrong, and im sure thats from a faulty differentiation, can you please let me know where i messed up...thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaction View Post
    i have just one more, about implicity differentiation...for this problem...

    x^3 + 5x^2y + 2y^2 = 4y + 11

    the last answer i came up with was...

    (-3x^2-10xy)/(5x^2+4y-1)

    then it wanted the slope of the tangent line at (1,2), but when i plugged these in the answer was wrong, and im sure thats from a faulty differentiation, can you please let me know where i messed up...thanks
    the 1 should be a 4. it comes from the derivative of 4y
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    Quote Originally Posted by Jhevon View Post
    the 1 should be a 4. it comes from the derivative of 4y
    ok, so then the rest of it is good then...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaction View Post
    ok, so then the rest of it is good then...
    yes. change that 1 to a 4 and you should be fine
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    Quote Originally Posted by Jhevon View Post
    yes. change that 1 to a 4 and you should be fine
    yeah i had it that way before, and just didnt do the basic algebra right, just gotta be careful for the really easy stuff to overlook...thanks alot
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