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 two functions in the product and find their derivatives. Let u = x^2+3x-1 and v = 2x-5. Differentiate u with respect to x: (du)/(dx) = (d)/(dx)(x^2+3x-1) = 2x+3 Differentiate v with respect to x: (dv)/(dx) = (d)/(dx)(2x-5) = 2 Step 2: Apply the product rule for differentiation, which states that if y=uv, then (dy)/(dx) = u(dv)/(dx) + v(du)/(dx). Substitute the expressions for u, v, (du)/(dx), and (dv)/(dx) into the product rule formula: (dy)/(dx) = (x^2+3x-1)(2) + (2x-5)(2x+3) Step 3: Expand and simplify the expression. (dy)/(dx) = 2(x^2+3x-1) + (2x-5)(2x+3) (dy)/(dx) = 2x^2+6x-2 + (4x^2+6x-10x-15) (dy)/(dx) = 2x^2+6x-2 + 4x^2-4x-15 Combine like terms: (dy)/(dx) = (2x^2+4x^2) + (6x-4x) + (-2-15) (dy)/(dx) = 6x^2+2x-17 The derivative is: (dy)/(dx) = 6x^2+2x-17 Send me the next one 📸