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Find the derivative of f(x) = sin(x) at x = π/2.
Find the derivative of f(x) = sin(x) at x = π/2.
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Practice Questions
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Q1
Find the derivative of f(x) = sin(x) at x = π/2.
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f'(x) = cos(x); f'(π/2) = cos(π/2) = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the derivative of f(x) = sin(x) at x = π/2.
Solution:
f'(x) = cos(x); f'(π/2) = cos(π/2) = 0.
Steps: 7
Show Steps
Step 1: Identify the function we want to differentiate, which is f(x) = sin(x).
Step 2: Recall the rule for finding the derivative of sin(x). The derivative of sin(x) is cos(x).
Step 3: Write down the derivative: f'(x) = cos(x).
Step 4: Now, we need to find the value of the derivative at x = π/2.
Step 5: Substitute π/2 into the derivative: f'(π/2) = cos(π/2).
Step 6: Calculate cos(π/2). The value of cos(π/2) is 0.
Step 7: Therefore, the derivative of f(x) = sin(x) at x = π/2 is 0.
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