Giulio Fagnano's trick Pretty clever..pic.twitter.com/7JpmjKqvkK
Show this thread
-
Isn't it more straightforward to derive the same through atan's derivative? atan(x) = ∫ˣ₀ 1/(1+t²) dt
Oh how great our vision is in hindsight! In a way, yes.. If you’re clever enough to come up with trig sub before it was invented.. or you knew the derivative or arctan(x) The beauty of this trick is that it doesn’t require anything except knowledge of derivatives
-
-
Well, the derivative of arctan is easy to come up with if you know tan's derivative and start with the identity f⁻¹(f(x)) = x The problem I have with your trick is that 1/cos²(t) appeared out of nowhere, I don't see what it teaches us and how to apply it elsewhere
-
To find the derivative of arctan you need inverse function theorem, or at the very least to prove the chain rule
- 8 more replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.