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
Welcome back — missed you this week. Here are the derivatives of the given functions. For the first function: Step 1: Write the given function. y = 4x^4 + 3x^3 + 2x^2 - 2x - 1 Step 2: Differentiate each term using the power rule, (d)/(dx)(ax^n) = anx^n-1. (dy)/(dx) = (d)/(dx)(4x^4) + (d)/(dx)(3x^3) + (d)/(dx)(2x^2) - (d)/(dx)(2x) - (d)/(dx)(1) Step 3: Apply the power rule to each term. (dy)/(dx) = (4 · 4x^4-1) + (3 · 3x^3-1) + (2 · 2x^2-1) - (2 · 1x^1-1) - 0 Step 4: Simplify the expression. (dy)/(dx) = 16x^3 + 9x^2 + 4x - 2 The derivative of the first function is: (dy)/(dx) = 16x^3 + 9x^2 + 4x - 2 For the second function: Step 1: Write the given function. F(x) = x^3 - x^2 - x + 1 Step 2: Differentiate each term using the power rule, (d)/(dx)(ax^n) = anx^n-1. F'(x) = (d)/(dx)(x^3) - (d)/(dx)(x^2) - (d)/(dx)(x) + (d)/(dx)(1) Step 3: Apply the power rule to each term. F'(x) = (1 · 3x^3-1) - (1 · 2x^2-1) - (1 · 1x^1-1) + 0 Step 4: Simplify the expression. F'(x) = 3x^2 - 2x - 1 The derivative of the second function is: F'(x) = 3x^2 - 2x - 1 Send me the next one 📸