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

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### 2 Answers

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`

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