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Find (dy)/(dx), when: y=(xcos^(-1)x)/(...

Find `(dy)/(dx)`, when:
`y=(xcos^(-1)x)/(sqrt(1-x^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`(xcos^(-1)x)/(sqrt(1-x^(2))).{(1)/(x)-(1)/((cos^(-1)x)sqrt(1-x^(2)))+(x)/((1-x^(2)))}`
`logy=logx+log cos^(-1)x-(1)/(2)log(1-x^(2))`
`rArr(1)/(2).(dy)/(dx)={(1)/(x)-(1)/(cos^(-1)x).(1)/(sqrt(1-x^(2)))-(1)/(2)xx((-2x))/((1-x^(2)))}`
`rArr(dy)/(dx)=y.{(1)/(x)-(1)/((cos^(-1)x)(sqrt(1-x^(2))))=(x)/((1-x^(2)))}.`
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