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.
Oh, I was thinking of it as 𝑦 = 𝑒𝑥 or 𝑥 = ln 𝑦, whose derivative in respect to 𝑦 is 𝑥 = 1/𝑦 (for 𝑦 > 0) or 𝑦 = 1/𝑥 (for 𝑥 > 0). Your interpretation is that the 𝑦-axis is non-existent or named differently, which is why I’d prefer the joke to say d/d𝑡 for less ambiguity, as @anothercatgirlsuggested.
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.
Nobody
exp(x)the y-derivation!The result is 𝑦 = ⅟ₓ, right?
No e^x doesn’t have a ‘y’ and so it also acts as a constant.
Oh, I was thinking of it as 𝑦 = 𝑒𝑥 or 𝑥 = ln 𝑦, whose derivative in respect to 𝑦 is 𝑥 = 1/𝑦 (for 𝑦 > 0) or 𝑦 = 1/𝑥 (for 𝑥 > 0). Your interpretation is that the 𝑦-axis is non-existent or named differently, which is why I’d prefer the joke to say d/d𝑡 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