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 1.a: Step 1: Rewrite the expression by dividing each term in the numerator by the denominator. Y = (3x^2 + 2x + 3)/(2x^2) Y = (3x^2)/(2x^2) + (2x)/(2x^2) + (3)/(2x^2) Y = (3)/(2) + (1)/(x) + (3)/(2)x^-2 Y = (3)/(2) + x^-1 + (3)/(2)x^-2 Step 2: Differentiate each term with respect to x. Recall that (d)/(dx)(c) = 0 for a constant c, and (d)/(dx)(x^n) = nx^n-1. (dY)/(dx) = (d)/(dx)((3)/(2)) + (d)/(dx)(x^-1) + (d)/(dx)((3)/(2)x^-2) (dY)/(dx) = 0 + (-1)x^-1-1 + (3)/(2)(-2)x^-2-1 (dY)/(dx) = -x^-2 - 3x^-3 Step 3: Rewrite the expression with positive exponents. (dY)/(dx) = -(1)/(x^2) - (3)/(x^3) The derivation is: -(1)/(x^2) - (3)/(x^3) Send me the next one 📸