यदि `y=sin^(-1)[xsqrt(1-x)-sqrtxsqrt(1-x^(2))]`
हो,तो `(dy)/(dx)` ज्ञात कीजिए।

Explanation

`y=sin^(-1)[xsqrt(1-x)-sqrtxsqrt(1-x^(2))]`
`rArry=sin^(-1)[sqrt(1-(sqrtx)^(2))-sqrtxsqrt(1-x^(2))]`
`x=sintheta` और `sqrtx=sinphi` रखने पर, ltbr gt`y=sin^(-1)[sinthetasqrt(1-sin^(2)phi)-sinphisqrt(1-sin^(2)theta)]`
`rArry=sin^(-1)[sinthetacosphi-sinphicostheta]`
`rArry=sin^(-1)[sin(theta-phi)]`
`rArry=theta-phi`
`rArry=sin^(-1)x-sin^(-1)sqrtx`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`(dy)/(dx)=d/(dx)(sin^(-1)x)-d/(dx)(sin^(-1)sqrtx)`
`(du)/(dx)=1/(sqrt(1-x^(2)))-1/(1-(sqrtx)^(2)).d/(dx)(sqrtx)`
`(dy)/(dx)=1/(sqrt(1-x^(2)))-1/(1-x)xx1/(2sqrtx)`
`therefore(dy)/(dx)=1/(sqrt(1-x^(2)))-1/(2sqrtx(1-x))`