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
Welcome back ThegirlGodishelping🥰💙🫠 — missed you this week. To solve this, we will find the derivative of the given expression (6x^2 - 1) with respect to x. We will use the chain rule. Step 1: Identify the outer and inner functions. Let y = (u), where u = 6x^2 - 1. Step 2: Differentiate the outer function with respect to u. The derivative of (u) is (1)/(u). (d)/(du)((u)) = (1)/(u) Step 3: Differentiate the inner function with respect to x. The derivative of 6x^2 - 1 is 12x. (du)/(dx) = (d)/(dx)(6x^2 - 1) = 12x Step 4: Apply the chain rule. The chain rule states that (dy)/(dx) = (dy)/(du) · (du)/(dx). Substitute the results from Step 2 and Step 3: (dy)/(dx) = (1)/(6x^2 - 1) · 12x (dy)/(dx) = (12x)/(6x^2 - 1) The derivative of (6x^2 - 1) is: (12x)/(6x^2 - 1) What's next? Send 'em! 📸