a. The definition of the inverse hyperbolic cosine is y = cosh -1 x x =

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a. The definition of the inverse hyperbolic cosine is y = cosh-1 x ⇔ x = cosh y, for x ≥ 1, 0 ≤ y < ∞. Use implicit differentiation to show that :(cosh¯x) = 1/Vx² – 1. dx

b. Differentiate sinh-1 x = ln (x + √x2 + 1) to show that d/dx (sinh-1 x) = 1/√x2 + 1.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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