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Continuity and Differentiability
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Derivative of $\tan^{-1}\left(\dfrac{1-x}{1+x}\right)$ with respect to $x$ is: (a) $-\dfrac{1}{1+x^2}$ (b) $\dfrac{1}{1+x^2}$ (c) $-\dfrac{1}{1-x^2}$ (d) $\dfrac{1}{1-x^2}$
Step-by-Step Solution
d/dx[\pi/4 - tan^{-1} x] = -1/(1+x^2). [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Selecting $-\dfrac{1}{1+x^2}$: 1.0 Mark
Correct Answer:$-\dfrac{1}{1+x^2}$
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