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Thread: Derivatives of hyperbolic trigonometric functions

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    Member Vinod's Avatar
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    Derivatives of hyperbolic trigonometric functions

    (a) If $cosh (y) = x + x^3y,$

    then at the point (1, 0) we y'=
    A. 0, B. −1, C. 1, D. 3, E. Does not exist.
    This is multiple choice question.
    The answer is (b). I don't know how it is computed. If any member explain me, it would be good help.
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    Forum Admin topsquark's Avatar
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    Re: Derivatives of hyperbolic trigonometric functions

    Quote Originally Posted by Vinod View Post
    (a) If $cosh (y) = x + x^3y,$

    then at the point (1, 0) we y'=
    A. 0, B. −1, C. 1, D. 3, E. Does not exist.
    This is multiple choice question.
    The answer is (b). I don't know how it is computed. If any member explain me, it would be good help.
    $\displaystyle \frac{d}{dx}( cosh(y) ) = sinh(y) \cdot \frac{dy}{dx}$

    So we know that
    $\displaystyle sinh(y) \cdot \frac{dy}{dx} = 1 + 3x^2 y + x^3 \frac{dy}{dx}$

    Now, for y = 0 we have $\displaystyle sinh(0) = \frac{e^0 - e^{-0}}{2} = 0$

    So what is dy/dx?

    -Dan
    Thanks from Vinod
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