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By James B. H. Storm

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8-5 Fig. 8-4 0 FUNCTIONS If x = sinh g, then y = sinh-1 x is called the inverse hyperbolic sine of x. Similarly we define the The inverse hyperbolic functions are multiple-valued and. as in the other inverse hyperbolic functions. case of inverse trigonometric functions [sec page 171 we restrict ourselves to principal values for which they ean be considered as single-valued. The following list shows the principal values [unless otherwise indicated] of the inverse hyperbolic functions expressed in terms of logarithmic functions which are taken as real valued.

8-5 Fig. 8-4 0 FUNCTIONS If x = sinh g, then y = sinh-1 x is called the inverse hyperbolic sine of x. Similarly we define the The inverse hyperbolic functions are multiple-valued and. as in the other inverse hyperbolic functions. case of inverse trigonometric functions [sec page 171 we restrict ourselves to principal values for which they ean be considered as single-valued. The following list shows the principal values [unless otherwise indicated] of the inverse hyperbolic functions expressed in terms of logarithmic functions which are taken as real valued.

52 d(u 2 v * w -c . 57 d(cosu) = - sinu = du PARTIAL x and y. 59 with derivatives of higher order respect of f(x,y) is defined dx =Ax Extension and x constant, a2f of more than to be a df ax 0 ay 9 a2f -=ayiG ayax and its partial a af 7~ 0 ay a af 0 derivatives as = $dx + $dy dy = Ay. to functions is defined as follows. 61 will be equal if the function case the order of differentiation makes no difference. dvkdwe... 55 with As examples + vdu vdu = to those for derivatives. two variables are exactly analogous.

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