This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the second derivative, we will use the result from the previous problem for the first derivative and apply the product rule. Step 1: Recall the first derivative. Let y = ((6x^2+1)^3 (2x-5)^4)/((x^3-2x+1)^2). The first derivative, (dy)/(dx), was found using logarithmic differentiation: (dy)/(dx) = y ( (36x)/(6x^2+1) + (8)/(2x-5) - (2(3x^2-2))/(x^3-2x+1) ) Step 2: Define A(x) for clarity. Let A(x) = (36x)/(6x^2+1) + (8)/(2x-5) - (2(3x^2-2))/(x^3-2x+1). Then the first derivative can be written as (dy)/(dx) = y A(x). Step 3: Apply the product rule to find the second derivative. The second