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
Step 1: Identify the function and apply the chain rule. Given y = (5 + 2 x). Let u = 5 + 2 x. Then y = u. The chain rule states that (dy)/(dx) = (dy)/(du) · (du)/(dx). Step 2: Differentiate y with respect to u. (dy)/(du) = (d)/(du)( u) = (1)/(u) Step 3: Differentiate u with respect to x. (du)/(dx) = (d)/(dx)(5 + 2 x) The derivative of a constant (5) is 0. The derivative of 2 x is 2 x. (du)/(dx) = 0 + 2 x = 2 x Step 4: Substitute u back and multiply the derivatives. (dy)/(dx) = (1)/(5 + 2 x) · (2 x) (dy)/(dx) = (2 x)/(5 + 2 x) The derivative is (2 x)/(5 + 2 x). 3 done, 2 left today. You're making progress.