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

Jul 23, 2014

You can think of the quotient rule in this terms:

("top"/"bottom")'=("top"'times"bottom"-"bottom"'times "top")/"bottom"^2.

See Quotient Rule . Thus in this case

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

which simplifies to $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{- 2 {e}^{x}}{{e}^{x} - 1} ^ 2$.