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Question
`sin^-1 1/sqrt(x + 1)`
Solution
Let y = `sin^-1 1/sqrt(x + 1)`
∴ `"dy"/"dx" = "d"/"dx" (sin^-1 1/sqrt(x + 1))`
= `1/sqrt(1 - (1/sqrt(x + 1))^2) * "d"/"dx" 1/(x + 1)^2`
= `1/sqrt((x + 1 - 1)/(x + 1)) * "d"/"dx" (x + 1)^2`
= `sqrt((x + 1)/x) * (-1)/2(x + 1)^((-3)/2)`
= `(-1)/(2sqrt(x)) * (1/(x + 1))`
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