Question

How do you differentiate `e^x/(x-1)` using the quotient rule?

Answer 1

Quotient rule states that for a function `y=f(x)/g(x)`, then `(dy)/(dx)=(f'(x)g(x)-f(x)g'(x))/g(x)^2`

Explanation:

Resolution:

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

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