Find the Derivative of the function: f(x)= ln(x^2/2x-3)
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To find the derivative of the function f(x) = ln(x^2/2x-3), you can use the chain rule of differentiation.
Step 1: Rewrite the function using logarithmic properties.
f(x) = ln(x^2) - ln(2x-3)
Step 2: Differentiate each term separately.
For the first term, ln(x^2), we can use the power rule of differentiation.
The derivative of ln(x^2) is (1/x^2) * (2x) = 2/x.
For the second term, ln(2x-3), we need to use the chain rule.
The derivative of ln(u) where u = 2x - 3 is (1/u) * u', where u' is the derivative of the inner function.
The derivative of 2x - 3 is 2.
Step 3: Combine the derivatives of the two terms.
The derivative of f(x) is therefore 2/x - 2/(2x-3).
So, the derivative of the function f(x) = ln(x^2/2x-3) is 2/x - 2/(2x-3).