What is the derivative of this function $y=xsin^-1x+sqrt(1-x^2)$ ?

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Answer 1 · 2016-08-05T12:44:45

$(dy)/(dx)=sin^(-1)x$

As $y=xsin^(-1)x+sqrt(1-x^2)$ , is sum of two functions, we can use product rule for first and chain rule for second. Hence,

$(dy)/(dx)=x xx1/sqrt(1-x^2)+1xxsin^(-1)x+1/(2sqrt(1-x^2))xx(-2x)$

= $x/sqrt(1-x^2)+sin^(-1)x-x/sqrt(1-x^2)$

= $sin^(-1)x$

What is the derivative of this function y=xsin^-1x+sqrt(1-x^2)y=xsin^-1x+sqrt(1-x^2)?