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30 May, 19:08

Find dy/dx by implicit differentiation xy=6

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Answers (2)
  1. 30 May, 22:34
    0
    dy/dx = - y/x

    Step-by-step explanation:

    xy = 6

    x * dy + y * dx = 0

    Subtract y dx from each side

    x dy = - y dx

    Divide each side by dx

    x dy / dx = - y dx/dx

    x dy/dx = - y

    Divide by x

    dy/dx = - y/x
  2. 30 May, 22:54
    0
    Step-by-step explanation:

    Apply the derivative operator d/dx to xy = 6. xy is a product, so we must use the product rule as well as the chain rule.

    dy/dx = - y/x

    (d/dx) (xy = 6) works out to x (dy/dx) + y (dx/dx) = 0, or just x (dy/dx) + y = 0.

    Solving this for dy/dx, we get, first, x (dy/dx) = - y, and then

    dy/dx = - y/x
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