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

Explanation

`(dy)/(dx)=sin^(-1)x`
`implies dy=sin^(-1)x.dx`
`implies int dy=int1. sin^(-1)x dx+c`
`implies y=sin^(-1)x.int1 dx-int((d)/(dx)sin^(-1)x)(int1.dx)dx+c`
`implies y=x sin^(-1)x`
`-int(x)/(sqrt(1-x^(2)))dx+c`
`impliesy=xsin^(-1)x-int(-dt)/(2sqrt(t))+c`
`implies y=x sin^(-1)x+(1)/(2)t^(-1//2)dt+c`
`implies y=x sin^(-1)x+sqrt(t)+c`
`implies y=xsin^(-1)x+sqrt(1-x^(2))+c`