TS EAMCET · Maths · Differentiation
If \(y=\cos ^{-1}\left(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}\right)\) then \(\frac{d y}{d x}=\)
- A \(\frac{2}{\sqrt{3 x-x^2-2}}\)
- B \(\frac{2}{3 x-x^2-2}\)
- C \(\frac{2}{\sqrt{2 x^2-6 x+5}}\)
- D \(\frac{2}{2 x^2-6 x+5}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{2 x^2-6 x+5}\)
Step-by-step Solution
Detailed explanation
\(y=\cos ^{-1}\left(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}\right)\) Let \(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}=v \Rightarrow \frac{d v}{d x}=\frac{6-4 x}{\left(2 x^2-6 x+5\right)^2}\) Now, \(y=\cos ^{-1} v \Rightarrow \frac{d y}{d x}=\frac{-1}{\sqrt{1-v^2}} \cdot \frac{d v}{d x}\)…
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