# How to find influence function of $\lambda=\log(\mu)$ such that $\mu=E(X)$?

The original question is that $$X$$ is a random variable that $$E(X)=\mu$$. We are interested in statistical functionals $$\theta=\int\log(x)dF(x)$$ and $$\lambda=\log(\mu)$$.

The first part of the question asks us to derive the influence function for $$\theta$$ which is simple, provided that $$\theta$$ is a linear functional. For the second part of the question, we are asked to derive the influence function for $$\log \mu$$ which puzzles me because $$\mu$$ is log of the expected value of $$X$$ which is linear. Could someone please show me how to derive the influence function in this case or gives me some hints?