Given `f(x)=(1-e^x)/(x+e^x)` what is f'(x).

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justaguide eNotes educator| Certified Educator

If the function is `f(x) = (1 - x*e^x)/(x + e^x)` , f'(x) can be determined using the quotient rule.

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

=> `(-x^2*e^x - x*e^x - x*e^(2x) - e^(2x) - 1 + x*e^x - e^x + x*e^(2x))/(x + e^x)^2`

=> `(-x^2*e^x - e^(2x) - 1 - e^x)/(x + e^x)^2`

The derivative `f'(x) = (-x^2*e^x - e^(2x) - 1 - e^x)/(x + e^x)^2`

dylzzz | Student

Thanks for your kindness.

Hoping for your answers for my future questions.

Thanks a lot eNotes and justaguide.

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