P Pedro123 Active Member Joined Jun 17, 2019 Messages 106 Gender Male HSC 2021 Aug 30, 2019 #1 Hey Guys, This is 1A Question 24 c) of the Cambridge Math 2012 3 unit textbook: If f is a differentiable function for all real x and has an inverse function g, prove that: Where f'(g(x)) is not 0
Hey Guys, This is 1A Question 24 c) of the Cambridge Math 2012 3 unit textbook: If f is a differentiable function for all real x and has an inverse function g, prove that: Where f'(g(x)) is not 0
fan96 617 pages Joined May 25, 2017 Messages 543 Location NSW Gender Male HSC 2018 Uni Grad 2024 Aug 30, 2019 #2 blyatman said: If denotes a derivative with respect to , then I'm not sure. Click to expand... This is fine, no? as
blyatman said: If denotes a derivative with respect to , then I'm not sure. Click to expand... This is fine, no? as
Trebla Administrator Administrator Joined Feb 16, 2005 Messages 8,401 Gender Male HSC 2006 Aug 30, 2019 #3 Same thing but another way to look at it: dy/dx = 1/(dx/dy) If y = g(x) and equivalently x = f(y) then g’(x) = 1/f’(y) and the result follows
Same thing but another way to look at it: dy/dx = 1/(dx/dy) If y = g(x) and equivalently x = f(y) then g’(x) = 1/f’(y) and the result follows
