Question

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

Answer 1

`f'(x)=(2e^x*(x-1))/(e^x-3x)^2`

Explanation:

Using the quotient rule we get
`f'(x)=((1-e^x)(e^x-3x)-(x-e^x)(e^x+3))/(e^x-3x)^2`
Multiplying out then we get
`f'(x)=(2e^x(x-1))/(e^x-3x)^2`