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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)?
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Practice Questions
1 question
Q1
For the function f(x) = x^2 + 2x + 1, what is f'(x)?
2x + 1
2x + 2
2x
x + 1
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f'(x) = 2x + 2.
Questions & Step-by-step Solutions
1 item
Q
Q: For the function f(x) = x^2 + 2x + 1, what is f'(x)?
Solution:
f'(x) = 2x + 2.
Steps: 9
Show Steps
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.
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