`x^(x)sin^(-1)sqrt()x` को xके सापेक्ष अवकलित कीजिए।

Explanation

माना कि `y=x^(x)sin^(-1)sqrt()x`
=uv , जहाँ `u=x^(x)` तथा `v=sin^(-1)sqrt()x` … (1)
अब `u=x^(x)rArrlogu=xlogx`
`rArr(1)/(u)*(du)/(dx)=x*(1)/(x)+1*logx`
`rArr(du)/(dx)=x^(x)(1+logx)` … (2)
तथा `v=sin^(-1)sqrt()xrArr(dv)/(dx)=(1)/(sqrt(1-x))xx(1)/(2sqrt(x))=(1)/(2sqrt(x-x^(2)))` ... (3)
(1) से, `(dy)/(dx)=u*(dv)/(dx)+(du)/(dx)*v`
`=x^(x)*(1)/(2sqrt(x-x^(2)))+x^(x)(1+logx)*sin^(-1)sqrt(x)` [(2) तथा (3) से]