Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/124

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Illustrative Example 2. Given , find by Leibnitz's Formula.

Solution. Let , and ;
then ,
  , ,
  , ,
  .   .   . .   .   .
  , .
Substituting in (17), we get

.

78. Successive differentiation of implicit functions. To illustrate the process we shall find from the equation of the hyperbola

.

Differentiating with respect to x, as in § 63,

,

or,

(A) .

Differentiating again, remembering that y is a function of x,

Substituting for its value from (A),

.

But from the given equation, .

.