`y = x sin^-1(x) + sqrt(1 - x^2)` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 57 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`y=xsin^-1(x) +sqrt(1-x^2)`

`y'=xd/(dx) sin^-1(x) + sin^-1(x) d/(dx) x + d/(dx)sqrt(1-x^2)`

`y'=x(1/sqrt(1-x^2)) + sin^-1(x) + (1/2)(1-x^2)^(-1/2)(-2x)`

`y'=x/sqrt(1-x^2) + sin^-1(x) +(-x)/sqrt(1-x^2)`

`y'=sin^-1(x)`

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