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Math Help - Hyperbolic derivative proof

  1. #1
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    Hyperbolic derivative proof

    When proving that d/dx (sinhx) = coshx, is this correct:

    sinhx = (e^x-e^-x) / 2
    d/dx sinhx = (e^x+e^-x)/2

    Since /2 is just a constant I can leave it like that, correct? Is there any steps that I migth be missing?
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  2. #2
    Moo
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    Hello,

    As 2 is a constant, yes you can.

    In general, the derivative of ay, where a is a constant will be a*y'
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Ok here we go

    sinh(x)=\frac{e^{x}-e^{-x}}{2}...therefore... \frac{D[sinh(x)]}{dx}=\frac{1}{2}[e^{x}+e^{-x}]=cosh(x)
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