letlim as x approaches 0 of (e^x + x)^(1/x)

attempted solution:

ln (e^x + x)^(1/x)

(1/x)(ln (e^x + x))

(1/x)ln (e^x) + (1/x)(ln x) ... do not use the product rule. Using L'Hopital, you take the derivative of ln(e^x + x) in the numerator over the derivative of x in the denominator

L'Hopital (derivative of the numerator over the derivative of the denominator) ...