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MathCalculus

Hyperbolic Cosine: Differentiate cosh(√x) and Check the Domain

Differentiate the hyperbolic cosine composite cosh(√x), check its real domain, and distinguish the interior derivative from an endpoint right-hand derivative.

Question

Differentiate the hyperbolic cosine function f(x)=cosh⁡(x)f(x)=\cosh(\sqrt{x}) with respect to xx, and check the real domains.

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Evidence boundary

This page solves the independently selected Exercise 9(b) in the University of Melbourne bridging notes over the real numbers. The printed answer gives the interior formula for x > 0. The endpoint right-hand derivative is a separately derived clarification, not an extra instruction attributed to the worksheet or a two-sided derivative of the given real-domain function.