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If y = sin^(-1)(x), what is dy/dx?

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Question: If y = sin^(-1)(x), what is dy/dx?

Options:

  1. 1/sqrt(1-x^2)
  2. 1/(1-x^2)
  3. sqrt(1-x^2)
  4. 1/x

Correct Answer: 1/sqrt(1-x^2)

Solution: 

The derivative of y = sin^(-1)(x) is dy/dx = 1/sqrt(1-x^2).

If y = sin^(-1)(x), what is dy/dx?

Practice Questions

Q1
If y = sin^(-1)(x), what is dy/dx?
  1. 1/sqrt(1-x^2)
  2. 1/(1-x^2)
  3. sqrt(1-x^2)
  4. 1/x

Questions & Step-by-Step Solutions

If y = sin^(-1)(x), what is dy/dx?
Correct Answer: dy/dx = 1/sqrt(1-x^2)
  • Step 1: Understand that y = sin^(-1)(x) means y is the angle whose sine is x.
  • Step 2: To find dy/dx, we need to use the derivative formula for the inverse sine function.
  • Step 3: The formula for the derivative of y = sin^(-1)(x) is dy/dx = 1/sqrt(1 - x^2).
  • Step 4: This formula tells us how y changes with respect to x.
  • Inverse Trigonometric Functions – Understanding the derivative of the inverse sine function, sin^(-1)(x), and its application in calculus.
  • Chain Rule – Applying the chain rule when differentiating functions involving inverse trigonometric functions.
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