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What is the derivative of \( y = \tan^{-1}(x) \)?

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Question: What is the derivative of \\( y = \\tan^{-1}(x) \\)?

Options:

  1. \\( \\frac{1}{1+x^2} \\)
  2. \\( \\frac{1}{x^2+1} \\)
  3. \\( \\frac{1}{x} \\)
  4. 0

Correct Answer: \\( \\frac{1}{1+x^2} \\)

Solution: 

The derivative of \\( y = \\tan^{-1}(x) \\) is \\( \\frac{1}{1+x^2} \\).

What is the derivative of \( y = \tan^{-1}(x) \)?

Practice Questions

Q1
What is the derivative of \( y = \tan^{-1}(x) \)?
  1. \( \frac{1}{1+x^2} \)
  2. \( \frac{1}{x^2+1} \)
  3. \( \frac{1}{x} \)
  4. 0

Questions & Step-by-Step Solutions

What is the derivative of \( y = \tan^{-1}(x) \)?
  • Step 1: Understand that we want to find the derivative of the function y = tan^(-1)(x).
  • Step 2: Recall that the derivative of a function gives us the rate of change of that function.
  • Step 3: Use the known formula for the derivative of the inverse tangent function, which is: d/dx(tan^(-1)(x)) = 1/(1+x^2).
  • Step 4: Apply this formula directly to our function y = tan^(-1)(x).
  • Step 5: Write down the result: The derivative of y = tan^(-1)(x) is y' = 1/(1+x^2).
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