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Solution for If Y = Sin − 1 ( 1 − X 2 1 + X 2 ) + Cos − 1 ( 1 − X 2 1 + X 2 ) , Find D Y D X ? - CBSE (Commerce) Class 12 - Mathematics

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Question

If \[y = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right),\text{ find } \frac{dy}{dx}\] ?

Solution

\[\text{ We have, y } = \sin^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right)\]

\[ \Rightarrow y = \frac{\pi}{2} \left[ \because \sin^{- 1} x + \cos^{- 1} x = \frac{\pi}{2} \right]\] \[\Rightarrow \frac{dy}{dx} = 0\]

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Solution If Y = Sin − 1 ( 1 − X 2 1 + X 2 ) + Cos − 1 ( 1 − X 2 1 + X 2 ) , Find D Y D X ? Concept: Simple Problems on Applications of Derivatives.
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