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
blyatman Well-Known Member Joined Oct 11, 2018 Messages 539 Gender Undisclosed HSC N/A Aug 30, 2019 #2 where I've assumed that If denotes a derivative with respect to , then I'm not sure.
fan96 617 pages Joined May 25, 2017 Messages 543 Location NSW Gender Male HSC 2018 Uni Grad 2024 Aug 30, 2019 #3 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
blyatman Well-Known Member Joined Oct 11, 2018 Messages 539 Gender Undisclosed HSC N/A Aug 30, 2019 #4 fan96 said: This is fine, no? as Click to expand... Yeh same thing, just wanted to write it with the d's to distinguish what we're differentiating w.r.t. Last edited: Aug 30, 2019
fan96 said: This is fine, no? as Click to expand... Yeh same thing, just wanted to write it with the d's to distinguish what we're differentiating w.r.t.
Trebla Administrator Administrator Joined Feb 16, 2005 Messages 8,110 Gender Male HSC 2006 Aug 30, 2019 #5 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