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Math Help - Implicit Differentiation

  1. #1
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    Implicit Differentiation

    Find dy/dx by implicit differentiation

    6(sin (8x))(cos (5y) = 4

    I tried doing it and came up with

    (tan (8x))(5 tan(5)), but this is not correct...
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  2. #2
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    Quote Originally Posted by tradar View Post
    I tried doing it and came up with

    (tan (8x))(5 tan(5)), but this is not correct...
    How did you arrive at your answer? What were your steps?

    Quote Originally Posted by tradar View Post
    Find dy/dx by implicit differentiation

    6(sin (8x))(cos (5y) = 4
    Applying the Product Rule and the Chain Rule, the differentiation would appear to start as:

    . . . . .6*(8 cos(8x) (dx/dx))*cos(5y) + 6*(sin(8x))*(-5 cos(5y) sin(5y) (dy/dx)) = 0

    . . . . .48 cos(8x) cos(5y) - 30 sin(8x) sin(5y) (dy/dx) = 0

    . . . . .48 cos(8x) cos(5y) = 30 sin(8x) sin(5y) (dy/dx)

    Divide through to isolate "dy/dx".
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  3. #3
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    8(tan8xtan5y) ?
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  4. #4
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    Quote Originally Posted by stapel View Post
    How did you arrive at your answer? What were your steps?


    Applying the Product Rule and the Chain Rule, the differentiation would appear to start as:

    . . . . .6*(8 cos(8x) (dx/dx))*cos(5y) + 6*(sin(8x))*(-5 cos(5y) sin(5y) (dy/dx)) = 0

    . . . . .48 cos(8x) cos(5y) - 30 sin(8x) sin(5y) (dy/dx) = 0

    . . . . .48 cos(8x) cos(5y) = 30 sin(8x) sin(5y) (dy/dx)

    Divide through to isolate "dy/dx".
    \frac{dy}{dx} = \frac{48cos(8x)cos(5y)}{30sin(8x)sin(5y)} = \frac{8cot(8x)cot(5y)}{5}
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