Determine using calculus dy/dx if y =arcsin x/(1-x^2)?

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We have to find the derivative of y = arc sin x/(1-x^2).

We use the quotient rule here:

y' = [(arc sin x)'*(1 - x^2) - ( arc sin x)*(1 - x^2)']/(1 - x^2)^2

=> [sqrt(1-x^2)*(1 - x^2) + 2x*(arc sin x)]/(1 - x^2)^2

The required derivative dy/dx = [sqrt(1-x^2)*(1 - x^2) + 2x*(arc sin x)]/(1 - x^2)^2

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