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Math Help - Find deltaz/deltax and deltaz/deltay?

  1. #1
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    Question Find deltaz/deltax and deltaz/deltay?

    here is what I am trying to do!

    R=ln(u^2 + v^2 + w^2)

    u= (x+2y)
    v=(2x-y)
    w=(2xy)

    find deltaz/deltax and deltaz/deltay when x=y=1

    This is a chain rule case correct? So:
    Dr/dx=(1/((x+2y)^2+(2x-y)^2+(2xy)^2))(2(x+2y)(1)+2(2x-y)(2)+2(2xy)(2y))
    Then placing 1 in all x and y makes:
    Dr/dx=(14/9)?

    And another one is:
    let x^2 +y^2 +z^2=3xyz
    find dz/dx and dz/dy

    for this do I isolate z and then find dz/dx and dz/dy?

    thanks!
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  2. #2
    MHF Contributor

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    Are you trying to find \frac{dr}{dx} or \frac{\Delta r}{\Delta x}? You say it is the latter but calculate the former.
    If you are looking for \frac{dr}{dx} then, yes, the chain rule is the right way to go.

    for the second, don't isolate z, use implicit differentiation: 2x+ 2z z_x= 3yz+ 3xyz_x. Solve for z_x. Do the same to find z_y.
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