MHT CET · Maths · Differentiation
If \(\mathrm{y}=\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) is equal to
- A \(\frac{5}{1+25 x^2}\)
- B \(\frac{1}{1+25 x^2}\)
- C \(\frac{1}{1+5 x^2}\)
- D \(\frac{5}{1+5 x^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{1+25 x^2}\)
Step-by-step Solution
Detailed explanation
\(y=\tan ^{-1}\left(\frac{5 x-x}{1+5 x \cdot x}\right)+\tan ^{-1}\left(\frac{\frac{2}{3}+x}{1-\frac{2}{3} x}\right)\) \(y=\left(\tan ^{-1}(5 x)-\tan ^{-1}(x)\right)+\left(\tan ^{-1}\left(\frac{2}{3}\right)+\tan ^{-1}(x)\right)\)
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