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Math Help - Hyperbolic functions #2

  1. #1
    Junior Member
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    Hyperbolic functions #2

    Calculate y' for:
    1. y= x sinh(x^2)
    I got to: y'= cosh x^2(2x) ....

    2. y= ln(cosh 3x)
    I got to: y= 1/cosh 3x (cosh 3x)
    = sinh 3/cosh 3x...
    I don't think these calculations are correct. Please help me. Thanks.
    Last edited by mr fantastic; October 5th 2009 at 04:30 AM. Reason: Re-titled post
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  2. #2
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    Hello, jsu03!

    You are making really strange errors . . .


    1)\;\;y \:=\: x\cdot\sinh(x^2)
    Product Rule . . .

    y' \;=\;x\cdot\cosh(x^2)\cdot2x + 1\cdot\sinh(x^2) \;=\;2x^2\!\cdot\cosh(x^2) + \sinh(x^2)




    2)\;\;y \:=\: \ln(\cosh 3x)
    Chain Rule . . .

    y' \;=\;\frac{1}{\cosh3x}\cdot\sinh3x\cdot 3 \;=\;\frac{3\sinh3x}{\cosh3x} \;=\;3\tanh3x

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