$\displaystyle (1+\ln x)^7$ I would have to use the general power rule rather than log properites correct . so the answer should be. $\displaystyle \frac{7}{x} (1 + \ln x)^6$
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You must use the chain rule $\displaystyle y=(1+\ln x)^7$ then $\displaystyle y'=7(1+\ln x)^6 \cdot (1+\ln x)' =7(1+\ln x)^6 \cdot \displaystyle\frac{1}{x} $
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