Two derivative problems! help

a) x/e^x
b) ln (e^x + ln x)
especially b
do not use logarithmic or implicit differentiation. thanks

a)you need to use the quotient rule here
first take the derivative of the numerator and multiply it by the donomenator


then subtract that by the derivative of the denomentator multiplied by the numerator
(1e^x)- (xe^x)

next take your denominator and square it, this is your new denomenator for your derivative.
[(1e^x)- xe^x] /e^2x

b) this requires chain rule. all you have to do is let "u" represent what is in the brackets of ln so you have ln(u)
next, take the derivative of ln(u)
=1/u

now multiply it by the derivative of "u" which is the derivative of (e^x + ln x)
= (e^x + 1/x)

now substitute the u for (e^x + ln x) from the first step

and now mutiply the derivatives
[1/(e^x + ln x)] (e^x + 1/x)