Explore BrainMass

Explore BrainMass

    Implicit Differentiation

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    If 2x^2 + 3xy = 12x + 5y, what is dy/dx?

    I put the x's on one side and got:

    2x^2 - 12 x = 3xy +5y

    then 4x - 12 = 3y + 5, but I'm not sure how to get a dy and dx.

    © BrainMass Inc. brainmass.com December 24, 2021, 6:52 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/implicit-differentiation-functions-146040

    SOLUTION This solution is FREE courtesy of BrainMass!

    2x^2 + 3xy = 12x + 5y
    To solve for dy/dx, you have to use implicit differentiation. Take d/dx of each side:
    d/dx (2x^2 + 3xy) = d/dx (12x + 5y)
    d/dx (2x^2) + d/dx (3xy) = d/dx (12x) + d/dx (5y)
    Taking derivatives:
    4x + 3(d/dx (xy)) = 12 + 5dy/dx
    Using the chain rule:
    4x + 3(xdy/dx + y) = 12 + 5dy/dx
    4x + 3xdy/dx + 3y = 12 + 5dy/dx
    Subtract 12:
    4x + 3xdy/dx + 3y - 12 = 5dy/dx
    Subtract 3xdy/dx:
    4x + 3y - 12 = 5dy/dx - 3xdy/dx
    Factor:
    4x + 3y - 12 = (5 - 3x)dy/dx
    Divide:
    dy/dx = (4x + 3y + 12)/(5 - 3x)

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 6:52 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/implicit-differentiation-functions-146040

    ADVERTISEMENT