Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
Find $\dfrac{dy}{dx}$ if $y = \tan^{-1}\left(\dfrac{3x - x^3}{1 - 3x^2}\right), -\dfrac{1}{\sqrt{3}} < x < \dfrac{1}{\sqrt{3}}$.
Step-by-Step Solution
Let $x = \tan \theta \Rightarrow y = 3\theta = 3\tan^{-1} x$. [1.5 Marks]
$\dfrac{dy}{dx} = \dfrac{3}{1+x^2}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Substituting $x = \tan\theta$: 1.5 Marks
Evaluating derivative $= 3/(1+x^2)$: 1.5 Marks
Correct Answer:
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