Find the Derivative - d/dx f(x) = natural log of 2x-3

Problem

d(ln(2*x−3))/d(x)

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, requiring the use of the Chain Rule.

2. Apply the formula for the derivative of ln(u) which is 1/u⋅d(u)/d(x)

3. Substitute u=2*x−3 into the derivative formula.

4. Differentiate the inner function 2*x−3 with respect to x which results in 2

5. Multiply the results to find the final derivative.

Final Answer

d(ln(2*x−3))/d(x)=2/(2*x−3)

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