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What is the derivative of y = sin^(-1)(x)?

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Question: What is the derivative of y = sin^(-1)(x)?

Options:

  1. 1/√(1-x^2)
  2. 1/(1+x^2)
  3. 1/(1-x^2)
  4. √(1-x^2)

Correct Answer: 1/√(1-x^2)

Solution: 

The derivative of y = sin^(-1)(x) is 1/√(1-x^2)

What is the derivative of y = sin^(-1)(x)?

Practice Questions

Q1
What is the derivative of y = sin^(-1)(x)?
  1. 1/√(1-x^2)
  2. 1/(1+x^2)
  3. 1/(1-x^2)
  4. √(1-x^2)

Questions & Step-by-Step Solutions

What is the derivative of y = sin^(-1)(x)?
  • Step 1: Understand that y = sin^(-1)(x) means y is the inverse sine function of x.
  • Step 2: Recall the formula for the derivative of the inverse sine function, which is dy/dx = 1/√(1 - x^2).
  • Step 3: Apply the formula directly to find the derivative of y = sin^(-1)(x).
  • Step 4: Write the final answer as dy/dx = 1/√(1 - x^2).
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