How to derive cosh (3x) in terms of cosh (x) and sinh (x) ? Initially I start with 1/2 (e^3x+e^-3x) but I'm stuck from there because I don't know how to continue... :(

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  1. Using the chain rule:

    u = 3 x

    du = 3 dx Divide both sides by 3

    du / 3 = dx

    dx = du / 3

    d cosh ( 3 x ) / dx =

    d cosh ( u ) / ( du / 3 ) =

    3 d cosh ( u ) / du

    d cosh ( u ) / du = sinh u


    d cosh ( 3 x ) / dx = 3 d cosh ( u ) / du = 3 sinh u = 3 sinh ( 3 x )

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  2. cosh(3x) = cosh(2x+x)
    = cosh2x coshx + sinh2x sinhx

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