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Math Help - solve for me this question please..

  1. #1
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    solve for me this question please..

    hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u
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  2. #2
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    Re: solve for me this question please..

    Quote Originally Posted by sharmala View Post
    hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u
    I assume your function is

    y= \frac{e^x - e^{-x}}{e^x + e^{-x}}

    so, what do you get for dy/dx using the quotient rule?


    fyi, calculus questions belong in the calculus forum. also, please using grouping symbols (parentheses) to make clear your expressions.
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    Re: solve for me this question please..

    Quote Originally Posted by sharmala View Post
    hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u
    Notice that \displaystyle \begin{align*} \frac{e^x - e^{-x}}{e^x + e^{-x}} = \tanh{x}  \end{align*}. So we have

    \displaystyle \begin{align*} y &= \tanh{x} \\ \frac{dy}{dx} &= \textrm{sech}^2\,{x} \\ &= 1 - \tanh^2{x} \\ &= 1 - y^2 \end{align*}
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