WBJEE · Maths · Inverse Trigonometric Functions
If \(y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log _e x}{1-6 \cdot \log _e x}\right]\), then \(\frac{d^2 y}{d x^2}=\)
- A 2
- B 1
- C 0
- D -1
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right] \\ & f(x)=\tan ^{-1}\left[\frac{1-2 \log x}{1+2 \log x}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-3 \cdot 2 \log…
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