AP EAMCET · Maths · Inverse Trigonometric Functions
If \(y=\operatorname{Tan}^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\operatorname{Tan}^{-1}\left(\frac{7 x}{1-12 x^2}\right)\), then at \(x=0, \frac{d y}{d x}=\)
- A \(6\)
- B \(7\)
- C \(9\)
- D \(10\)
Answer & Solution
Correct Answer
(D) \(10\)
Step-by-step Solution
Detailed explanation
\( y = 3 \operatorname{Tan}^{-1} x + \operatorname{Tan}^{-1}(4x) + \operatorname{Tan}^{-1}(3x) \) \( \frac{d y}{d x} = \frac{3}{1+x^2} + \frac{4}{1+(4x)^2} + \frac{3}{1+(3x)^2} \)…
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