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The derivative of \( y \) with respect to \( t \) for the function:

\[
y = \frac{2 + \ln t}{4 - \ln t}
\]

is:

\[
\frac{6}{t(\ln t - 4)^2}
\]

Would you like further clarification or details on this? Here are five related questions to consider:

1. What are the conditions for which this derivative is undefined?
2. How would you compute the second derivative of this function?
3. Can we interpret the behavior of the function \( y(t) \) near specific points, such as \( t = 1 \)?
4. How can we apply the chain rule if the variable \( t \) depends on another variable, say \( s \)?
5. What would the graph of \( y(t) \) and its derivative look like for a certain range of \( t \)?

**Tip:** When differentiating fractions, always check if you can apply the quotient rule or simplify first for easier computation.

Find the derivative of y with respect to t: y = (2 + ln(t)) / (4 - ln(t))

Learn how to compute the derivative of the function y = (2 + ln(t)) / (4 - ln(t)) with respect to t using the quotient rule. This step-by-step solution covers key calculus concepts such as the quotient rule and the derivative of natural logarithms. Suitable for college-level calculus students.

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