`sin^(-1)(2xsqrt(1-x^(2)))` का अवकलन x के सापेक्ष ज्ञात कीजिए यदि
`1/(sqrt2)ltxlt1`

Explanation

`1/(sqrt2)ltxlt1`
`rArr1/(sqrt2)ltsinthetalt1`
`rArrpi/4ltthetaltpi/2`
`rArr-pilt-2thetaltpi`
`rArr-pilt-2thetalt-pi/2`
`rArr0ltpi-2thetaltpi/2`
`thereforey=sin^(-1)[sin(pi-2theta)]` [समी (1) से]
`rArry=pi-2theta`
`rArry=pi-2sin^(-1)x`
`therefore(dy)/(dx)=0-2xx1/(sqrt(1-x^(2)))`
`rArr(dy)/(dx)=(-2)/(sqrt(1-x^(2)))`.