`(dy)/(dx)` निकालें यदि (Find `(dy)/(dx)ify=sin^(-1)((5x+12sqrt(1-x^(2)))/(13))`

Explanation

यहाँ `y=sin^(-1)[(5x+12sqrt(1-x^(2)))/(13)]`
`x=costheta` रखें तो `sqrt(1-x^(2))=sintheta`
`thereforey=sin^(-1)((5costheta+12sintheta)/(13))=sin^(-1)((12)/(13)"sin"theta+(5)/(13) "costheta)` … (1)
माना कि `(12)/(13)=cosalpha`, तब `(5)/(13)=sinalpha` तथा `tanalpha=(5)/(12)`
`therefore` समीकरण (1) से,
`y=sin^(-1)(cosalphasintheta+sinalphacostheta)`
`=sin^(-1)[(sinthetacosalpha+costhetasinalpha)]`
`=sin^(-1)[sin(theta+alpha)]=theta+alpha`
`=cos^(-1)x+tan^(-1)((5)/(12))`
`therefore(dy)/(dx)=(-1)/(sqrt(1-x^(2)))+0=(-1)/(sqrt(1-x^(2)))`