निम्नलिखित फलनों का x के सापेक्ष अवकलन कीजिए-
`sin(2sin^(-1)x)`

Explanation

`y=sin(2sin^(-1)x)`
माना `x=sintheta`, तब `theta=sin^(-1)x`
`thereforey=sin2theta`
`rArry=2sinthetacostheta`
`rArry=2xsqrt(1-x^(2))`,
`[becausecostheta=sqrt(1-sin^(2)theta)=sqrt(1-x^(2))]`
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`(dy)/(dx)=2d/(dx){x(sqrt(1-x^(2)))}`
`rArr(dy)/(dx)=2[xd/(dx)(sqrt(1-x^(2)))+(sqrt(1-x^(2)))d/(dx)(x)]`
`rArr(dy)/(dx)=2[x.1/2(1-x^(2))^(-1//2)d/(dx)(1-x^(2))+sqrt(1-x^(2)).1]`
`rArr(dy)/(dx)=2[x/(2sqrt(1-x^(2)))xx(-2x)+sqrt(1-x^(2))]`
`rArr(dy)/(dx)=2[(-x^(2))/(sqrt(1-x^(2)))+sqrt(1-x^(2))]`
`(dy)/(dx)=2[(-x^(2)+(1-x^(2)))/(sqrt(1-x^(2)))]`
`=(2(1-2x^(2)))/(sqrt(1-x^(2)))`