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Chain rule question

  1. Nov 23, 2009 #1
    Use the chain rule to compute the partials of
    F(z,w) = f(g_1(z,w),g_2(z,w),z,w)
    where f(x,y,z,w)=x^2 +y^2 +z^2 −w^2
    and g_1(z,w) = wcosz , g_2(z,w) = wsinz

    Evaluate the partials at z = 0, w = 1. Confirm your result by writing out F explicitly as a function of z and w, computing its partial derivatives, and then evaluating at the same point.

    I'm a little confused by the differentiation here:

    so x = wcosz, y = wsinz thus:
    x^2 = w^2cos^z
    y^2 = w^2sin^2z
    z = z^2
    w = -w^2

    what next?
  2. jcsd
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