Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then `g''f(x)` is equal to

Explanation

It is given that `g(x)` is the inverse of `f(x)`.

`:. g(f(x)) = x->(1)`

Differentiating both sides w.r.t. `x`,

`g'(f(x))f'(x) = 1->(2)`

`=>g'(f(x)) = 1/(f'(x)) ->(3)`

Again differentiating (2) w.r.t. `x`

`g'(f(x))f''(x) + f'(x)(g''f(x)f'(x)) = 0`

` f'(x)(g''f(x)f'(x)) = - g'(f(x))f''(x) `

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