Question

If \( y = \tan^{-1}(x) \), then \( \frac{dy}{dx} = \)

• A. \( \frac{1}{1 - x^2} \)
• B. \( \frac{1}{1 + x^2} \)
• C. \( 1 + x^2 \)
• D. \( 1 - x^2 \)

Hint:

The derivative of \( \tan^{-1}(x) \) is a commonly used result in calculus, and it simplifies to \( \frac{1}{1 + x^2} \).

Answer 1

The Correct Option is B

The derivative of \( y = \tan^{-1}(x) \) with respect to \( x \) is given by the standard derivative formula: \[ \frac{dy}{dx} = \frac{1}{1 + x^2}. \] This is a well-known formula for the derivative of the inverse tangent function.