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)) = -
Create a free account to view solution
View Solution FreeMore Differentiation Questions
If y = sec , then dy/dx equals-...If y = sin-1 and + p, then p is equal to...If f(x), g(x), h(x) are polynomials in x of degree 2 and F(x) = , then F′(x) is equal to...If y = sin (msin−1x), then (1 − x2) y2− xy1 + m2y equals to -...If f(x) = sin (log x) and y = f , then dy/dx equals-...