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
The derivative of x^3 + 2x is 3x^2 + 2. Steps: To find the derivative of f(x) = x^3 + 2x, we apply the sum rule and the power rule for differentiation. 1. Derivative of x^3: Using the power rule, (d)/(dx)(x^n) = nx^n-1. (d)/(dx)(x^3) = 3x^3-1 = 3x^2. 2. Derivative of 2x: Using the constant multiple rule and the power rule. (d)/(dx)(2x) = 2 · (d)/(dx)(x^1) = 2 · 1x^1-1 = 2 · 1x^0 = 2 · 1 = 2. 3. Sum Rule: The derivative of a sum of functions is the sum of their derivatives. (d)/(dx)(x^3 + 2x) = (d)/(dx)(x^3) + (d)/(dx)(2x) (d)/(dx)(x^3 + 2x) = 3x^2 + 2.