this post was submitted on 08 Nov 2025
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Reminds me of a fun joke!
A constant and e^x were walking down the street. They see a differentiator coming, and instantly the constant gets scared shitless. The differentiator comes up, and as expected, POOF, the constant is gone. e^x starts laughing and says "nice try, can't touch me". But the differentiator tips his hat and responds "is that right?", then throws off his coat and shows that he is d/dy.
The result is ๐ฆโ=โโ โ, right?
No e^x doesn't have a 'y' and so it also acts as a constant.
Oh, I was thinking of it as ๐ฆโ= ๐^๐ฅ^ or ๐ฅโ= ln ๐ฆ, whose derivative in respect to ๐ฆ is ๐ฅโ= 1/๐ฆ (for ๐ฆโ> 0) or ๐ฆโ= 1/๐ฅโ(for ๐ฅ > 0). Your interpretation is that the ๐ฆ-axis is non-existent or named differently, which is why I'd prefer the joke to say d/d๐ก for less ambiguity, as @anothercatgirl suggested.
yayaya, or in other cases like multiple independent variables, I'm not sure because it's been 6 years since I took calculus
The general form would be implicit differentiation! d/dx dx/dy e^x = e^x dx/dy