A Calendar of Leading Experiments

Cover A Calendar of Leading Experiments
A Calendar of Leading Experiments
William S Willaiam Suddards Franklin
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167 is satisfied by both equations (i) and (2); and, inasmuch as the rules for differentiating are not usually understood by the student, especially when applied to such general equations as (i) and (2), the following discussion is arranged to appeal to one's funda- mental arithmetical sense. Awkwardness of notation is the chief difficulty, as usual, and one must remember the following points : If y increases always u times as fast as x, then u is called the derivative of y with respect to x. I...f y depends on x as the only variable, the derivative is represented by the symbol dy/dx. If y depends on more than one variable, the derivative with respect to x is called a partial derivative and it is usually represented by the symbol dy/dx. The two symbols dy/dx and dy/dx have, however, precisely the same arithmetical mean- ing; thus in the first case y actually increases dy/dx times as fast as x, and in the second case y would increase dy/dx times as fast as x if x only, among all the variables upon which y depends, were allowed to change.

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