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
To find (dy)/(dx) for the given function, we first simplify the expression for y. Step 1: Simplify the expression for y. The numerator x^2 + 4x + 4 is a perfect square trinomial, which can be factored as (x+2)^2. y = (x^2 + 4x + 4)/(x + 2) y = ((x+2)^2)/(x + 2) Assuming x ≠ -2, we can cancel out one (x+2) term from the numerator and denominator. y = x + 2 Step 2: Differentiate y with respect to x. Now, we find the derivative of y = x+2. (dy)/(dx) = (d)/(dx)(x + 2) Using the power rule (d)/(dx)(x^n) = nx^n-1 and the constant rule (d)/(dx)(c) = 0: (dy)/(dx) = 1 · x^1-1 + 0 (dy)/(dx) = 1 · x^0 + 0 (dy)/(dx) = 1 · 1 + 0 (dy)/(dx) = 1 The derivative is: (dy)/(dx) = 1 Send me the next one 📸