DERIVATIVES

In the following formulas u, v, w represent functions of x , and a, c, n represent fixed real numbers. All arguments in the trigonometric functions are measured in radians, and all inverse trigonometric and hyperbolic functions represent principal values.

Let y= f(x) and define, respectively, a function and its derivative for any value x that is their common domain. The differential for the function at such a value x is accordingly defined as

Each derivative formula has an associated differential formula. For example, formula 6 above has the differential formula

where the binomial coefficient, n the nonnegative integer, and .

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28. , ( u>1, cosh ^?1 u>0)

29. , ( u ²<1)

30. , ( u ²>1)

31. , (0< u<1, sech ^?1 u>0)

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33. , [ p constant]

34. , [ q constant]

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