Question

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

Answer 1

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

Explanation:

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`