Originally Posted by
Jhevon you're completely wrong (sorry for being so blunt, but you asked). first you didn't even differentiate, second, you didn't split up the log correctly. the correct way to do this is by the chain rule.
the chain rule says, if we have a composite function f(g(x)), its derivative is given by f ' (g(x))*g'(x). in this case we have a composite function, we can think of ln(x) as f(x) and e^-x + xe^-x as g(x)
y = ln(e^-x + xe^-x)
=> y' = 1/(e^-x + xe^-x) * (-e^-x + e^-x -xe^-x) ..........we have to use the product rule to differentiate the xe^-x
=> y' = (-e^-x + e^-x -xe^-x)/(e^-x + xe^-x)
=> y' = (-xe^-x)/(e^-x + xe^-x)