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CBSE Class 12 Math 2019 All India Set 1 Solved Paper

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Question : 2 of 29
Marks: +1, -0
If y=sin⁡−1x+cos⁡−1xy=\sin^{-1} x+\cos^{-1} x, find dydx\frac{dy}{dx}.
Solution:  
y=sin⁡−1x+cos⁡−1xy=\sin^{-1} x+\cos^{-1} x
⇒dydx=ddx(sin⁡−1x+cos⁡−1x)\Rightarrow \frac{dy}{dx}=\frac{d}{dx}(\sin^{-1} x+\cos^{-1} x)
=ddx(sin⁡−1x)+ddx(cos⁡−1x)=\frac{d}{dx}(\sin^{-1} x)+\frac{d}{dx}(\cos^{-1} x)
=11−x2−11−x2=\frac{1}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-x^2}}
=0=0
Therefore, dydx=0\frac{dy}{dx}=0
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