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Find the derivative of f(x) = tan(x). (2022) 2022

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Question: Find the derivative of f(x) = tan(x). (2022) 2022

Options:

  1. sec^2(x)
  2. csc^2(x)
  3. sec(x)
  4. tan^2(x)

Correct Answer: sec^2(x)

Exam Year: 2022

Solution: 

The derivative f\'(x) = d/dx(tan(x)) = sec^2(x).

Find the derivative of f(x) = tan(x). (2022) 2022

Practice Questions

Q1
Find the derivative of f(x) = tan(x). (2022) 2022
  1. sec^2(x)
  2. csc^2(x)
  3. sec(x)
  4. tan^2(x)

Questions & Step-by-Step Solutions

Find the derivative of f(x) = tan(x). (2022) 2022
  • Step 1: Understand that we want to find the 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: it is sec^2(x).
  • Step 4: Write down the result: f'(x) = sec^2(x).
  • Differentiation of Trigonometric Functions – Understanding how to differentiate basic trigonometric functions, specifically the tangent function.
  • Chain Rule Application – Recognizing that the derivative of tan(x) involves the secant function and its square.
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