Step 1: Identify the function f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1.
Step 2: Find the derivative of the function, f'(x).
Step 3: Use the power rule to differentiate each term: The derivative of x^4 is 4x^3, the derivative of -4x^3 is -12x^2, the derivative of 6x^2 is 12x, and the derivative of -4x is -4.
Step 4: Combine the derivatives to get f'(x) = 4x^3 - 12x^2 + 12x - 4.
Step 5: Substitute x = 1 into the derivative: f'(1) = 4(1)^3 - 12(1)^2 + 12(1) - 4.
Step 6: Calculate each term: 4(1) = 4, -12(1) = -12, 12(1) = 12, and -4 = -4.
