Give a much shorter, concise version — just the essential steps and the final answer, no padding. Problem: What is the derivative of x³ + 2x with respect to x? Give a full worked solution with steps. Current solution: The derivative of x³ + 2x with respect to x is 3x² + 2. Full Worked Solution: To find the derivative of f(x) = x³ + 2x, we will use the following differentiation rules: 1. Sum Rule: (d)/( dx)[g(x) + h(x)] = (d)/(dx)[g(x)] + (d)/(dx)[h(x)] 2. Power Rule: (d)/(d x)[xⁿ] = nxⁿ⁻¹ 3. Constant Multiple Rule: (d)/(dx)[cf(x)] = c(d)/(dx)[f(x)] Let f (x) = x³ + 2x. Step 1: Apply the Sum Rule We can differentiate each term separately: (d)/(dx)(x³ + 2x) = ddx(x³) + (d)/(dx)(2x) Step 2: Differentiate the first term, x³ Using the Power Rule where n=3: (d)/(dx)(x³) = 3x³⁻¹ = 3x² Step 3: Differentiate the second term, 2x Using the Constant Multiple Rule and the Power Rule (where x = x¹, so n=1): (d)/(dx)(2x) = 2 · (d)/(dx)(x¹) (d)/(dx)(x¹) = 1x¹⁻¹ = 1x⁰ = 1 · 1 = 1 So, (d)/(dx) (2x) = 2 · 1 = 2 Step 4: Combine the results Substitute the derivatives of each term back into the expression from Step 1: (d)/(d x)(x³ + 2x) = 3x² + 2