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Suppose that the dependent variables z and w are functions of the independent variables x and y, defined by the equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0, where fz gw – fw gz = 1. Which one of the following is correct?
  • a)
    zx = fw gx – fx g
  • b)
    zx = fx gw – fw g
  • c)
    zx = fz gx – fx g
  • d)
    zx = fz gw – fz gx
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Suppose that the dependent variables z and w are functions of the inde...
fx = fz zx + fw wx      ...(1) 
gx = gz zx + gw wx            ...(2) 
Multiply (1) and (2) by gw and fw respectively, then subtract, we obtain 
fx gw – gx fw = (fz gw – gz fw)z
but fz gw = fw gz = 1, then 
zx = fx gw – gx fw
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Community Answer
Suppose that the dependent variables z and w are functions of the inde...
The equations f(x, y, z, w) = 0 and g(x, y, z, w) = 0 imply that the partial derivatives of f with respect to z and w, denoted by fz and fw, and the partial derivatives of g with respect to z and w, denoted by gz and gw, are all zero.

So, fz = 0, fw = 0, gz = 0, and gw = 0.
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