find the derivative of y= ln\sqrt((2x+1)/(x^(2)-4) )  at x=4

We are given the function:

\[
y = \ln\sqrt{\frac{2x+1}{x^2 - 4}}
\]

### Step 1: Simplify the Expression

We can simplify the logarithmic function first. Using the property of logarithms \( \ln(\sqrt{A}) = \frac{1}{2} \ln(A) \), we rewrite the function as:

\[
y = \frac{1}{2} \ln \left( \frac{2x+1}{x^2 - 4} \right)
\]

### Step 2: Apply the

Find the derivative of y = ln√((2x+1)/(x^2 - 4)) at x = 4

Learn how to differentiate the logarithmic function y = ln√((2x+1)/(x^2 - 4)) at x = 4, using key calculus concepts such as the chain rule, quotient rule, and logarithmic differentiation. This advanced calculus problem is suitable for Grades 11-12.

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