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Question
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
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Solution
Let, y = `sin^(–1)(xsqrtx)`
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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