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Partial Derivatives

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that z=f(ax+by), where a and b are constants. Show that bz(x) = az(y).

    z(x) means partial derivative of z with respect to x, as for z(y).

    2. Relevant equations

    3. The attempt at a solution

    Say z=ax+by

    z(x) = a

    z(y) = b

    So bz(x) = ba = ab = az(y)

    I'm not sure that this is a correct analysis - because I know f(ax+by) doesn't necessarily mean z = ax+by... How should I interpret this problem?
  2. jcsd
  3. Apr 24, 2010 #2


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    Homework Helper

    Keep f general and use the chain rule. It might help to let u = ax + by.
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