Final answer:
The derivative of ln(4x-1) is 4/(4x-1), which is found by applying the chain rule to the natural logarithm function and its inner function 4x-1.
Step-by-step explanation:
The derivative of ln(4x-1) is determined using the chain rule, which is a method for finding the derivative of composite functions. To use the chain rule, we first look at the outer function, which in this case is the natural logarithm (ln) function, and then we multiply by the derivative of the inner function, which is 4x-1.
Since the derivative of ln(u) is 1/u where u is a function of x, and the derivative of 4x-1 is 4, applying the chain rule gives:
The derivative of ln(4x-1) = 1/(4x-1) × 4 = 4/(4x-1).
This result shows how to compute the slope of the tangent line to the curve y = ln(4x-1) at any point x.