She is derivation, a transform of functions that describes rate of 𝑓(𝑥) changing as 𝑥 changes. (This can be represented visually as the slope of the graph 𝑦 = 𝑓 (𝑥).) He is the exponential function 𝑒𝑥, which is the only* non-zero function whose derivative is itself - in other words, unaffected by derivation. The number 𝑒 is a constant (around 2.718) and the base of natural logarithms, hence the title.
* except its multiples such as −2 𝑒𝑥, which are… just… uh… derivative works
But the derivative of e^x+c is just e^x (which for c!=0 is not the same). That’s why the +c is added during integrating because all +c is derived to 0 and thus indistinguishable.
She is derivation, a transform of functions that describes rate of 𝑓(𝑥) changing as 𝑥 changes. (This can be represented visually as the slope of the graph 𝑦 = 𝑓 (𝑥).) He is the exponential function 𝑒𝑥, which is the only* non-zero function whose derivative is itself - in other words, unaffected by derivation. The number 𝑒 is a constant (around 2.718) and the base of natural logarithms, hence the title.
* except its multiples such as −2 𝑒𝑥, which are… just… uh… derivative works
Much appreciated!
https://i.kym-cdn.com/photos/images/original/000/913/758/a12.jpg
I think you forgot about e^x + 1, and e^x + 2, and … …
(My profs always dunked on me for forgetting the + c and I can’t resist doing it to someone else, I’m sorry)
For real tho, great explanation
But the derivative of e^x+c is just e^x (which for c!=0 is not the same). That’s why the +c is added during integrating because all +c is derived to 0 and thus indistinguishable.
I wish I could say I commented this late at night or something, but nope I’m just dumb lmao thanks