यदि `f(x) =sqrt (x^(2) +1 ,)g(x) =(x+1 ) /(x^(2)+1 ) ` व् ` h(x) =2x -3` तब ` f'[h'{g '(x) }]` का मान ज्ञात कीजिए|

Explanation

` " "f(x) =sqrt(x^(2) +1)`
` rArr" "f'(x)= (1)/(2) (x^(2)+1)^(1//2) (2x) =(x)/(sqrt(x^(2)+1 ))" "...(1)`
` " "g(x) =(x+1)/(x^(2)+1)`
` rArr " "g' (x) =((x^(2)+1)*1-(x+1)*2x) /((x^(2)+1)^(2))`
` " "= (-x^(2)-2x +1)/((x^(2)+1)^(2))" "...(2)`
तथा ` " "h(x) =2x -3`
`rArr " "h' (x) =2 `
इसलिए ` f'[h '{g'(x)}]=f'[h'((-x^(2)-2x+1)/((x^(2)+1)^(2)))]`
` " "= f '(2) " "` [समीकरण (2 ) से ]
` " "= (2)/(sqrt(2^(2)+1))=(2)/(sqrt(5))" "` [समीकरण (1 )से ]