Final answer:
The derivative of the function sqrt(9x-4) using the chain rule is D. (9/2)/√9x-4, which represents the slope of the tangent to the curve at any point x.
Step-by-step explanation:
The question seeks the derivative of the function f(x) = sqrt(9x-4). When calculating the derivative of a function involving a square root, we must apply the chain rule. To begin, we express the square root as a fractional power, so the function becomes f(x) = (9x - 4)^(1/2). The derivative of this function using the chain rule is:
f'(x) = (1/2)(9x - 4)^(-1/2) × (9)
After simplification, we get:
f'(x) = (9/2)(9x - 4)^(-1/2), which can be written as D. (9/2)/√9x-4
This derivative represents the slope of the tangent to the curve of f(x) at any given point x.