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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    Hi,

    I have the following equation:

    ln(8y)+6xy=ln(sin(4x))

    After differentiating I get:

    (1/8y)(dy/dx)+6y+6x*(dy/dx)=(4cos(4x))/sin(4x)

    And with this, I need to work out dy/dx at (0,0)

    When I try this it seems messy and I get zero. Can someone explain where I have gone wrong please

    Many thanks
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  2. #2
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    Quote Originally Posted by Bryn View Post
    Hi,

    I have the following equation:

    ln(8y)+6xy=ln(sin(4x))

    After differentiating I get:

    (1/8y)(dy/dx)+6y+6x*(dy/dx)=(4cos(4x))/sin(4x)

    And with this, I need to work out dy/dx at (0,0)

    When I try this it seems messy and I get zero. Can someone explain where I have gone wrong please

    Many thanks
    Dear Bryn,

    Note that the equation, ln(8y)+6xy=ln(sin(4x)) is not defined when y=o since ln(0) is not defined. Therefore you cannot find \frac{dy}{dx} at (0,0)

    Hope this will help you.
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