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If f(x) = x^2 + 2x + 1, find f'(1).
If f(x) = x^2 + 2x + 1, find f'(1).
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Practice Questions
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Q1
If f(x) = x^2 + 2x + 1, find f'(1).
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f'(x) = 2x + 2, thus f'(1) = 2(1) + 2 = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = x^2 + 2x + 1, find f'(1).
Solution:
f'(x) = 2x + 2, thus f'(1) = 2(1) + 2 = 4.
Steps: 7
Show Steps
Step 1: Identify the function f(x) = x^2 + 2x + 1.
Step 2: Find the derivative of the function f(x). The derivative f'(x) tells us the rate of change of f(x).
Step 3: Use the power rule to differentiate each term: The derivative of x^2 is 2x, the derivative of 2x is 2, and the derivative of 1 is 0.
Step 4: Combine the derivatives to get f'(x) = 2x + 2.
Step 5: Now, we need to find f'(1). This means we will substitute x = 1 into the derivative f'(x).
Step 6: Substitute x = 1 into f'(x): f'(1) = 2(1) + 2.
Step 7: Calculate the result: f'(1) = 2 + 2 = 4.
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