1. ## Differentiation

Differentiate:
${\frac{1-xe^x}{x+e^x}}$

I'm new to this stuff and this one seems to be a bit tricky. If you could please break it down step by step that would be very helpful.

2. Originally Posted by Neversh
Differentiate:
${\frac{1-xe^x}{x+e^x}}$

I'm new to this stuff and this one seems to be a bit tricky. If you could please break it down step by step that would be very helpful.
Use the Quotient Rule

$\frac{dy}{dx} = \frac{(x + e^x)\frac{d}{dx}(1 - xe^x) - (1 - xe^x)\frac{d}{dx}(x + e^x)}{(x + e^x)^2}$

$= \frac{(x + e^x)(-e^x - xe^x) - (1 - xe^x)(1 + e^x)}{(x + e^x)^2}$

$= \frac{-e^x(x + e^x)(1 + x) - (1 - xe^x)(1 + e^x)}{(x + e^x)^2}$