Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
The derivative of $\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$ with respect to $x$ for $|x| < 1$ is:
(a) $\dfrac{2}{1 + x^2}$
(b) $\dfrac{1}{1 + x^2}$
(c) $\dfrac{2}{\sqrt{1 - x^2}}$
(d) $\dfrac{-2}{1 + x^2}$
Step-by-Step Solution
$\dfrac{d}{dx}[2\tan^{-1} x] = \dfrac{2}{1+x^2}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating derivative $= 2/(1+x^2)$: 1.0 Mark
Correct Answer: $\dfrac{2}{1 + x^2}$
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