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 derivation for question 6.a: Step 1: Expand the given expression. Y = (2x - 4)(x^2 + 2x) Y = 2x(x^2) + 2x(2x) - 4(x^2) - 4(2x) Y = 2x^3 + 4x^2 - 4x^2 - 8x Y = 2x^3 - 8x Step 2: Differentiate the expanded expression with respect to x. Recall that (d)/(dx)(ax^n) = nax^n-1. (dY)/(dx) = (d)/(dx)(2x^3) - (d)/(dx)(8x) (dY)/(dx) = 2(3)x^3-1 - 8(1)x^1-1 (dY)/(dx) = 6x^2 - 8x^0 (dY)/(dx) = 6x^2 - 8 The derivative is: 6x^2 - 8 3 done, 2 left today. You're making progress.