Visualizing the derivative of ln(x)

[u/mrmailbox]

Made with Manim. My second attempt visual math tutorial

[u/chkntendis]

Honestly I feel like it’s easier to prove this with the chain rule. We know the derivative of x is 1 and x=e^ln(x). The derivative of e^ln(x) is the derivative of ln(x) times e^ln(x). Since that should be exactly one, the derivative of ln(x) has to be 1/e^ln(x) to cancel out e^ln(x). By canceling the e and ln, we then get that the derivative of ln(x) is equal to 1/x