For the function f(x) = x^2 + 2x + 1, what is f'(x)?

For the function f(x) = x^2 + 2x + 1, what is f'(x)?

Step 1: Identify the function f(x) = x^2 + 2x + 1.
Step 2: Recognize that we need to find the derivative of f(x), which is denoted as f'(x).
Step 3: Use the power rule for derivatives: If f(x) = x^n, then f'(x) = n*x^(n-1).
Step 4: Apply the power rule to each term in f(x):
- For the first term x^2, the derivative is 2*x^(2-1) = 2x.
- For the second term 2x, the derivative is 2.
- The third term 1 is a constant, and its derivative is 0.
Step 5: Combine the derivatives from each term: f'(x) = 2x + 2 + 0.
Step 6: Simplify the expression: f'(x) = 2x + 2.

Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Polynomial Functions – Understanding how to differentiate polynomial functions, which are functions of the form f(x) = ax^n + bx^(n-1) + ... + k.