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Question
Differentiate the following w.r.t. x : `sin^-1(x^(3/2))`
Solution
Let y = `sin^-1(x^(3/2))`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[sin^-1(x^(3/2))]`
= `(1)/sqrt(1 - (x^(3/2))^2)."d"/"dx"(x^(3/2))`
= `(1)/sqrt(1 - x^3) xx 3/2x^(1/2)`
= `(3sqrt(x))/(2sqrt(1 - x^3)`
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