निम्नलिखित फलनों का x के सापेक्ष अवकलन कीजिए-
`sin[cos(x^(2))]`.

Explanation

माना `y=sin[cos(x^(2))]`
`therefore(dy)/(dx)=d/(dx){sin[cos(x^(2))]}`
`=d/(dx)(sint),[cos(x^(2))=t` रखने पर`]`
`=d/(dt)(sint)(dt)/(dx)`
`=costd/(dx)(cosx^(2))`
`=cos[cos(x^(2))]d/(dx)(cosu),[x^(2)=u` रखने पर`]`
`=cos[cos(x^(2))]d/(du)(cosu)(du)/(dx)`
`=cos[cos(x^(2))](-sinu)d/(dx)(x^(2))`
`=cos[cos(x^(2))](-sinx^(2)).2x`
`=-2xsinx^(2)cos[cos(x^(2))]`
विकल्पतः `d/(dx)[sin(cosx^(2))]`
`=cos(cosx^(2))d/(dx)(cosx^(2))`
`=cos(cosx^(2))(-sinx^(2))d/(dx)(x^(2))`
`=cos(cosx^(2))(-sinx^(2))(2x)`
`=-2xsinx^(2)cos(cosx^(2))`