Question

How do you differentiate `f(x) = (x^2-4x)/(e^x+1)` using the quotient rule?

Answer 1

The 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:

`(dy)/(dx)=((2x-4)(e^x-1)-(x^2-4x)(e^x))/(e^x+1)^2`

`(dy)/(dx)=((2xe^x-4e^x-2x+4)-x^2e^x+4xe^x)/(e^x+1)^2`

`(dy)/(dx)=(e^x(-x^2+6x-4)-2x+4)/(e^x+1)^2`