Several Differentiation Formulas of Special Functions. Part VI
نویسندگان
چکیده
The papers [11], [13], [1], [15], [2], [8], [9], [16], [5], [12], [10], [4], [6], [7], and [14] provide the notation and terminology for this paper. In this paper x denotes a real number and Z denotes an open subset of R. One can prove the following propositions: (1) Suppose Z ⊆ dom((the function tan) ·(the function cot)). Then (i) (the function tan) ·(the function cot) is differentiable on Z, and (ii) for every x such that x ∈ Z holds ((the function tan) ·(the function cot))′ Z (x) = 1 (the function cos)((the function cot)(x))2 · − 1 (the function sin)(x)2 . (2) Suppose Z ⊆ dom((the function tan) ·(the function tan)). Then (i) (the function tan) ·(the function tan) is differentiable on Z, and (ii) for every x such that x ∈ Z holds ((the function tan) ·(the function tan))′ Z(x) = 1 (the function cos)((the function tan)(x))2 · 1 (the function cos)(x)2 . (3) Suppose Z ⊆ dom((the function cot) ·(the function cot)). Then (i) (the function cot) ·(the function cot) is differentiable on Z, and (ii) for every x such that x ∈ Z holds ((the function cot) ·(the function cot))′ Z (x) = 1 (the function sin)((the function cot)(x))2 · 1 (the function sin)(x)2 . (4) Suppose Z ⊆ dom((the function cot) ·(the function tan)). Then (i) (the function cot) ·(the function tan) is differentiable on Z, and
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تاریخ انتشار 2008