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Find dy/dx if y = sin^(-1) (2x/1+x²) | Differentiation of sin inverse 2x upon 1 + x square

The derivative of `sin^(-1)((2x)/(1+x^(2)))` with respect to `cos^(-1)((1-x^(2))/(1+x^(2)))` is

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Q18 | If sin^2⁡x + cos^2⁡y = 1 find dy/dx | Implicit Function | If sin square x + cos square y = 1

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proof that sin^2(x)=(1-cos2x)/2 || 1-cos2x=2sin^2 x