DifferentiationHard
Question
Let g(x) be the inverse of an invertible function f(x) which is differentiable for all real x, then g″(f(x)) equals to
Options
A.
B.
C.
D.None of these
Solution
Given that g-1(x) = f(x)
⇒ x = g(f(x)) or g′(f(x)) f′(x) = 1
⇒ g′(f(x)) =
⇒ g″(f(x)) . f′(x) =
⇒ g″(f(x)) = -
⇒ x = g(f(x)) or g′(f(x)) f′(x) = 1
⇒ g′(f(x)) =
⇒ g″(f(x)) . f′(x) =
⇒ g″(f(x)) = -
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