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
Here's the solution for the question with options 1, 2, 3, and 4 (Question 63). 63. If y = (x^2), find (dy)/(dx). Step 1: Identify the functions for the chain rule. Let u = x^2. Then y = (u). Step 2: Find the derivatives of y with respect to u and u with respect to x. (dy)/(du) = (d)/(du)( u) = u (du)/(dx) = (d)/(dx)(x^2) = 2x Step 3: Apply the chain rule, (dy)/(dx) = (dy)/(du) · (du)/(dx). (dy)/(dx) = ( u) · (2x) Step 4: Substitute u = x^2 back into the expression. (dy)/(dx) = 2x (x^2) The correct option is 1. 2x (x^2). That's 3 down. 2 left today — send the next one.