How do you use the quotient rule to find the derivative of $y = \frac{e^{x} + 1}{e^{x} - 1}$ $y=(e^x+1)/(e^x-1)$ ?

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Answer 1 · 2014-07-23T22:05:46

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 $dy/dx=(-2e^x)/(e^x-1)^2$ .

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