The image shows mathematical functions involving natural logarithms ($\ln$) that require differentiation. Would you like a step-by-step explanation for one or all of these problems? For example, I can solve problems 51 through 60 systematically.

Let me know which specific problems you'd like me to address! Here are your options:

1. Would you like the derivative of all these functions solved?
2. Are you looking for a detailed explanation of logarithmic differentiation?
3. Should I rewrite these equations for easier reference?
4. Would you prefer hints for solving them yourself?
5. Should I focus on a subset, like the first five or the last five problems?

Tip: Remember that logarithmic properties like $\ln(a/b) = \ln a - \ln b$ and $\ln(a^b) = b \ln a$ are often key to simplifying these problems before differentiating!