Giulio Fagnano's trick Pretty clever..pic.twitter.com/7JpmjKqvkK
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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
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Sure, but the (proposed) alternative is all of integral calculus
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How so? No integration is done
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