Answer
= 2
Work Step by Step
We use the rule for taking the derivative of a natural log and chain rule to obtain:
f(x) = ln(x + lnx)
f'(x) = $\frac{(x + lnx)'}{x + lnx}$
f'(x) = $\frac{1 + \frac{1}{x}}{x + lnx}$
f'(1) = $\frac{1 + \frac{1}{1}}{1 + ln1}$
f'(1) = $\frac{1 +1}{1 + 0}$
f'(1) = $\frac{2}{1}$
f'(1) = 2
