AP EAMCET · Maths · Differentiation
If \(y=\tan \left(3 \tan ^{-1} x\right)\), then\(\left(1-3 x^2\right) \frac{d^2 y}{d x^2}-12 x \frac{d y}{d x}=\)
- A \(6(x+y)\)
- B \(6(y-x)\)
- C \(6 y\)
- D \(-6 x\)
Answer & Solution
Correct Answer
(B) \(6(y-x)\)
Step-by-step Solution
Detailed explanation
\(y=\tan \left(3 \tan ^{-1} x\right)\) Let \(\tan ^{-1} x=\theta\) \(\Rightarrow \quad \tan \theta=x\) \(\therefore \quad y=\tan 3 \theta=\frac{3 \tan \theta-\tan ^3 \theta}{1-3 \tan ^2 \theta}\) \(=\frac{3 x-x^3}{1-3 x^2}\) \(\Rightarrow\left(1-3 x^2\right) y=3 x-x^3\) On…
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