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B Differentiating by two different variables -- when is it okay?

  1. Jun 10, 2017 #1
    I'm working through the problems in Mary Boas's Mathematical Methods text. Here's how she began solving one problem...

    "We take differentials of the equation 1/i + 1/o = 1/f (f=constant) to get
    -di/i2 - do/o2 = 0."

    So on the left side the first term was differentiated with respect to i and the second term was differentiated with respect to o. Why is it okay to differentiate these terms by different variables? I'm only used to differentiating by one variable at a time.
  2. jcsd
  3. Jun 10, 2017 #2


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    In general it is not OK.
    In this case we can justify the step by first differentiating both sides wrt ##o## to get
    then multiply both sides by ##do##
  4. Jun 11, 2017 #3
    I get it. Thanks very much!
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