# How do you use the quotient rule to find the derivative of y=(e^x+1)/(e^x-1) ?

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$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left({e}^{x} + 1\right) ' \left({e}^{x} - 1\right) - \left({e}^{x} - 1\right) ' \left({e}^{x} + 1\right)}{{e}^{x} - 1} ^ 2 = \frac{{e}^{x} \left({e}^{x} - 1\right) - {e}^{x} \left({e}^{x} + 1\right)}{{e}^{x} - 1} ^ 2$
which simplifies to $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 2 {e}^{x}}{{e}^{x} - 1} ^ 2$.