If y=^{-1} x, then \;dy/dx=

Correct Answer is : 11+x2\;1/1+x²1+x21

Correct Answer is : 11+x2\;1/1+x²1+x21

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AP ICET 2024 6th May 2024 Shift 1

Question : 161 of 200

Marks: +1, -0

y=\tan^{-1} x

\;\frac{dy}{dx}=

Solution:

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.

Quick Tip

The derivative of

\tan^{-1}(x)

is a commonly used result in calculus, and it simplifies to

\frac{1}{1+x^2}

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