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If g is inverse of f then prove that f''...

If g is inverse of f then prove that `f''(g(x))=-g''(x)(f'(g(x)))^(3).`

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Since g is inverse of f,f(g(x))=x
`therefore" "f'(g(x))g'(x)=1" (1)"`
`rArr" "f'(g(x))=(1)/(x'(g))`
`rArr" " f''(g(x))g'(x)=-(g''(x))/(g'(x))^(2)`
`rArr" " f''(g(x))=-(g''(x))/(g'(x))^(3)`
`rArr" "f''(g(x))=-g''(x)(f'(g(x)))^(3)`
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