Question

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

Answer 1

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

`dy/dx=((e^x+1)'(e^x-1)-(e^x-1)'(e^x+1))/(e^x-1)^2=(e^x(e^x-1)-e^x(e^x+1))/(e^x-1)^2`

which simplifies to `dy/dx=(-2e^x)/(e^x-1)^2`.