음(sinh-1(x)) = EXAMPLE 4 Prove that + x2 SOLUTION Let y = sinh-(x). Then sinh(y) = x. If we differentiate this equation implicitly with respect to x, we get dy dx = 1. Since cosh?(y) - sinh?(y) = 1 and cosh(y) 2 0, we have cosh(y) = V1 + sinh?(y), so 1. dy dx 1 cosh(y) V1+ sinh?(y)

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