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Math Help - Derivative of Hyperbolic Function

  1. #1
    Senior Member nycmath's Avatar
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    Derivative of Hyperbolic Function

    I must find d/dx of the function in the picture. I get a different answer than the textbook. Can someone explain, based on my picture, what I did wrong?
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  2. #2
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    Re: Derivative of Hyperbolic Function

    The hyperbolic half-angle formula:

    $\sinh(x) = \text{sgn}(x)\sqrt{\dfrac{\cosh(2x)-1}{2}}$

    Square both sides, and you find that your answer is equal to the textbook's answer. Check out hyperbolic trig identities. Better yet, try to prove them on your own.
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    Re: Derivative of Hyperbolic Function

    Quote Originally Posted by nycmath View Post
    I must find d/dx of the function in the picture. I get a different answer than the textbook. Can someone explain, based on my picture, what I did wrong?
    Is it possible that the two solution are equivalent?
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  4. #4
    Senior Member nycmath's Avatar
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    Re: Derivative of Hyperbolic Function

    Thanks. Great to know that my answer is correct.
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  5. #5
    Senior Member nycmath's Avatar
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    Re: Derivative of Hyperbolic Function

    I squared both sides and found out that my answer matches the textbook answer. I never knew that trig half-angle formulas extended into the hyperbolic topic.
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