Question

How do you differentiate `f(x)= e^x/(x-3 )` using the quotient rule?

Answer 1

`d/(dx) (e^x/(x-3)) = (e^x(x-4))/(x-3)^2`

Explanation:

The quotient rule states that:

`d/(dx)( f(x)/g(x) )= (f'(x)g(x) -f(x)g'(x))/(g(x))^2`

For `f(x) = e^x` and `g(x) = x-3` we have:

`d/(dx) (e^x/(x-3)) = (e^x(x-3) - e^x)/(x-3)^2 = (e^x(x-4))/(x-3)^2`