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  • Find dy / dx , if y = sin ^ -1 x + sin ^-1 1− x ^ 1 / 2

Q 13    Find dy/dx   if y = sin ^{-1} x + sin^{-1} \sqrt{1- x^2} , 0 <x< 1

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Given function is 
y = sin ^{-1} x + sin^{-1} \sqrt{1- x^2} , 0 <x< 1
Now, differentiate w.r.t. x 
\frac{dy}{dx}= \frac{d(sin ^{-1} x + sin^{-1} \sqrt{1- x^2})}{dx} = \frac{1}{\sqrt{1-x^2}}+\frac{1}{\sqrt{1-(\sqrt{1-x^2})^2}}.\frac{d(\sqrt{1-x^2})}{dx}\\ \frac{dy}{dx}= \frac{1}{\sqrt{1-x^2}}+\frac{1}{\sqrt{1-1+x^2}}.\frac{1}{2\sqrt{1-x^2}}.(-2x)\\ \\ \frac{dy}{dx}= \frac{1}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-x^2}}\\ \frac{dy}{dx}= 0
Therefore, differentiate w.r.t. x  is 0

Posted by

Gautam harsolia

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