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 $\displaystyle \displaystyle \begin{align*} \frac{e^x - e^{-x}}{e^x + e^{-x}} = \tanh{x} \end{align*}$. So we have
$\displaystyle \displaystyle \begin{align*} y &= \tanh{x} \\ \frac{dy}{dx} &= \textrm{sech}^2\,{x} \\ &= 1 - \tanh^2{x} \\ &= 1 - y^2 \end{align*}$