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What is the first derivative of f(x) = tan(x)? (2021)

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Question: What is the first derivative of f(x) = tan(x)? (2021)

Options:

  1. sec^2(x)
  2. cos^2(x)
  3. sin^2(x)
  4. csc^2(x)

Correct Answer: sec^2(x)

Exam Year: 2021

Solution: 

The derivative of f(x) = tan(x) is f\'(x) = sec^2(x).

What is the first derivative of f(x) = tan(x)? (2021)

Practice Questions

Q1
What is the first derivative of f(x) = tan(x)? (2021)
  1. sec^2(x)
  2. cos^2(x)
  3. sin^2(x)
  4. csc^2(x)

Questions & Step-by-Step Solutions

What is the first derivative of f(x) = tan(x)? (2021)
  • Step 1: Understand that we want to find the first derivative of the function f(x) = tan(x).
  • Step 2: Recall the basic rule for finding the derivative of the tangent function.
  • Step 3: The derivative of tan(x) is a known result in calculus.
  • Step 4: Write down the result: the derivative of tan(x) is sec^2(x).
  • Step 5: Therefore, we can conclude that f'(x) = sec^2(x).
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