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Find the derivative of f(x) = tan(x) at x = 0.
Find the derivative of f(x) = tan(x) at x = 0.
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Practice Questions
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Q1
Find the derivative of f(x) = tan(x) at x = 0.
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f'(x) = sec^2(x); f'(0) = sec^2(0) = 1.
Questions & Step-by-step Solutions
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Q
Q: Find the derivative of f(x) = tan(x) at x = 0.
Solution:
f'(x) = sec^2(x); f'(0) = sec^2(0) = 1.
Steps: 7
Show Steps
Step 1: Identify the function we want to differentiate, which is f(x) = tan(x).
Step 2: Recall the derivative formula for the tangent function. The derivative of tan(x) is f'(x) = sec^2(x).
Step 3: Now, we need to find the derivative at a specific point, which is x = 0.
Step 4: Substitute x = 0 into the derivative formula: f'(0) = sec^2(0).
Step 5: Calculate sec(0). Since sec(x) = 1/cos(x), and cos(0) = 1, we have sec(0) = 1/1 = 1.
Step 6: Now, calculate sec^2(0): sec^2(0) = (sec(0))^2 = 1^2 = 1.
Step 7: Therefore, the derivative of f(x) = tan(x) at x = 0 is f'(0) = 1.
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