Question

How do you differentiate `f(x) = (e^x-4x)/(1-xe^x)` using the quotient rule?

Answer 1

`f'(x)=(e^x+e^(2x)-4x^2e^x-4)/(1-xe^x)^2`

Explanation:

By the Quotient rule

`f'(x)=((e^x-4)(1-xe^x)-(e^x-4x)(-e^x-xe^x))/(1-xe^x)^2`
simplifying we get the result above.