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Question
Differentiate w.r.t. x the function:
`sin^(–1)(xsqrtx ), 0 ≤ x ≤ 1`
Solution
Let, `y = sin^-1 (x sqrtx)`
On differentiating with respect to x,
`dy/dx = 1/ sqrt (1 - x^3). d/dx x sqrtx`
`= 1/ sqrt(1 - x^3). [x . 1/(2 sqrtx) + sqrtx]`
`= 1/ sqrt(1 - x^3) [sqrtx/2 + sqrtx]`
`= 1/sqrt (1 - x^3) [(sqrtx + 2sqrtx)/2]`
`= 3/2 * sqrt(x/(1 - x^3))`
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