1.

If `y=sin^(-1)x+sin^(-1)sqrt(1-x^(2))`, what is `(dy)/(dx)` equal to?A. `cos^(-1)x+cos^(-1)sqrt(1-x^(2))`B. `(1)/(cosx)+(1)/(cos sqrt(1-x^(2)))`C. `(pi)/(2)`D. 0

Answer» Correct Answer - D
Given function is :
`y=sin^(-1)x+sin^(-1)sqrt(1-x^(2))`
On differentiating, w.r.t. x, we get
`(dy)/(dx)=(1)/(sqrt(1-x^(2)))+(1)/(sqrt(1-1+x^(2))).(1)/(2sqrt(1-x^(2)))(-2x)`
`=(1)/(sqrt(1-x^(2)))-(1)/(sqrt(1-x^(2)))=0`


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