humble moon
This is he proof to d/dx arcsin.
Everything makes perfect sense up to when arccos = (1-sin(y)^2)^1/2
I understand that those numbers in the identity of arccos using Pythagoras a^2+b^2=c^2 -> sin^2+cos^2 = 1^2
Thant makes sense.
My questions is why do we use the identity?
Why don’t we just use 1/(arccos) as the answer?
What’s with the extra step turning 1/(arccos) into 1/(1-arcsin^2)^1/2?
mortal kindleBOT
inner dome
This is he proof to d/dx arcsin.
Everything makes perfect sense up to when arcc...
Because its in terms of y
Where you would want in x
humble moon
Yah but, this may just be. A lack of understand of inverse functions, but cos = x. Why not just use that
Why the extra step
inner dome
Also I see you used chain rule, but you differentiated arcsin to arccos without prove, the correct way is to take arcsin of both sides
inner dome
Yah but, this may just be. A lack of understand of inverse functions, but cos = ...
Wdym
humble moon
1/(arccos) = 1/x
inner dome
No
inner dome
inner dome
You also differentiated arcsin wrong
This will differential will not give any meaningful result...
Also the trig identity has arcos in it which is wrong lol
humble moon
Ya
I haven’t learned much about derivative manipulation yet
I just extrapolated my understanding of trig to try and find a proof to the inverse trig functions
My very wrong method actually is pretty accurate to finding the identities when I forget lol.
Also you lost me on the second image
icy terrace
yup thats implicit differentiation
