Derivatives of Tangent and Reciprocal Trigonometric Functions

provided that cos(x) 0 and so the two formulas for the derivative are equivalent for all x in the domain of f(x) 1 + tan(x) Therefore, we can find the roots of the function f' (x) = cos(x) + sin(x) using either expression. sec(x The function f has a horizontal tangent f f' (x) = 0, which happens when 1 + tan(x) = 0 or, equivalently, when tan(x ... ................
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