Several Differentiation Formulas of Special Functions . Part
نویسندگان
چکیده
(Def. 2) cosec = 1 the function sin . For simplicity, we follow the rules: x, a, b, c are real numbers, n is a natural number, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. One can prove the following propositions: (1) If (the function cos)(x) 6= 0, then sec is differentiable in x and (sec)′(x) = (the function sin)(x) (the function cos)(x)2 . (2) If (the function sin)(x) 6= 0, then cosec is differentiable in x and (cosec)′(x) = − (the function cos)(x) (the function sin)(x)2 . (3) ( 1 x) n Z = 1 xZ . (4) Suppose Z ⊆ dom sec . Then sec is differentiable on Z and for every x such that x ∈ Z holds (sec)′ Z(x) = (the function sin)(x) (the function cos)(x)2 .
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