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differentiate the following function with respect to x (1) cos^-1(2x (sqrt(1-x^2))),1/root(2)

differentiate the following function with respect to x
(1) cos^-1(2x (sqrt(1-x^2))),1/root(2) < x <1

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
6 years ago

y=cos-12xv(1-x2)

dy/dx=-1/v{1-4x2(1-x2)}.2{x.(-2x)/2v(1-x2)+v(1-x2)}

=-1/v(4x4-4x2+1).2[-x2/v(1-x2) +v(1-x2)]

={-2/v(2x2-1)2 }.{-x2+1-x2}/v(1-x2)

=-2(-2x2+1)/{(2x2-1).v(1-x2)}

=2(2x2-1)/{(2x2-1).v(1-x2) }

=2/v(1-x2)

Thanks & regards

Rinkoo Gupta

AskIITians Faculty

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