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What is the derivative of f(x) = x^2 at x = 3?
Practice Questions
Q1
What is the derivative of f(x) = x^2 at x = 3?
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Questions & Step-by-Step Solutions
What is the derivative of f(x) = x^2 at x = 3?
Steps
Concepts
Step 1: Identify the function we want to find the derivative of, which is f(x) = x^2.
Step 2: Use the power rule for derivatives. The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).
Step 3: Apply the power rule to f(x) = x^2. Here, n = 2, so f'(x) = 2*x^(2-1) = 2*x^1.
Step 4: Simplify the derivative. f'(x) = 2x.
Step 5: Now, we need to find the derivative at x = 3. Substitute 3 into the derivative: f'(3) = 2*3.
Step 6: Calculate the result: 2*3 = 6.
No concepts available.
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