InterviewSolution
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InterviewSolution
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`x^(x)sin^(-1)sqrt()x` को xके सापेक्ष अवकलित कीजिए। |
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Answer» 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] |
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