`sin^(-1)(xsqrt(x)),0 le x le 1` – InterviewSolution

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1.	`sin^(-1)(xsqrt(x)),0 le x le 1`
Answer» Let `y=sin^(-1)(xsqrt(x))` `implies(dy)/(dx)=(d)/(dx)sin^(-1)(xsqrt(x))` `=(1)/(sqrt(1-(xsqrt(x))^(2)))(d)/(dx)(xsqrt(x))` `=(1)/(sqrt(1-x^(3)))(d)/(dx)(x^(3//2))` `=((3)/(2)x^(1//2))/(sqrt(1-x^(3)))=(3sqrt(x))/(2sqrt(1-x^(3)))`

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