The Internet’s Missing Derivative

I take the derivative of the factorial function using a classic LAWN trick. Let me know if you enjoyed this wonderful calculus problem or if you have any suggested problems for me to take a look at.

[thefirstuwu]

First the gamma of 1/2 is sqrt(pi), then the derivative of the gamma function of 1 is negative Euler-Mascheroni constant. What next? The integral of gamma function of 2 is the Feigenbaum constant?

[varunnadgir]

How do you get a negative derivative at the point x=1 if the factorial function is increasing at the point x=1? Shouldn't the derivative be positive?

[jacobstarr]

Well obviously it’s just 1! Which is just 1 😂😂😂

[redbrixanimations]

This math is much too complex for me 😂 maybe I’ll understand this one or two years from now

[khandelkompani]

In statistical physics:
Use Stirling approximation
ln(x!) ≈ x ln(x) - x
d/dx (ln(x!)) ≈ ln(x)
(1/x!) d/dx (x!) ≈ ln(x)
d/dx (x!) ≈ x! ln(x)
LOL 😂

[UnePintade]

Casually swapping derivative and indefinite integral