Question-212464

Question Number 212464 by liuxinnan last updated on 14/Oct/24

Commented by liuxinnan last updated on 14/Oct/24

i s i t r i g h t

Answered by MrGaster last updated on 14/Oct/24

The above process is .

correct Let me explain ite

her .

Firstly given the functionalr

elationship y = f (x) and its inverse

function x = φ (y) .

According to the

derivativeformula fore

invers functions we knowa

tht if y = f (x), then f^{'} (x) = \frac{d y}{d x} Similarly for the inversec

funtion x = φ (y), we have

φ^{'} (y) = \frac{d x}{d y}

S ince x and y are in a reciprocali

relationshp as inversei

functons, \frac{d y}{d x} and \frac{d x}{d y} are reciprocals of each

otherwhich means :

φ^{'} (x) = \frac{d x}{d y} = \frac{1}{\frac{d y}{d x}} = \frac{1}{f^{'} (x)}

Next, since x = φ (y), we can substitute x with φ (y), thus obtaining :

φ^{'} (y) = \frac{1}{f^{'} [φ (y)]}

Commented by liuxinnan last updated on 15/Oct/24

t h a n k s