What is e (2.718…) and why does it literally appear everywhere?
In: 756
So I’ve always been confused by that, but this got me to dive in and I think I have it figured out.
First, e is very similar to pi. It’s simply a mathematical constant that just exists. There’s no real satisfying rhetoric that makes it makes sense, it only really makes sense with mathematical proofs/equations
Second, it’s important to know what a derivative is. It’s basically the slope of a curve, but at a specific point. Think the original line is speed, and the derivative line is acceleration.
So go to Desmos.com/calculator
1. Copy and paste these two equations in two separate boxes (looks crazy, but just paste it in the calculator and it should look clean). These are 2^x and the derivative of 2^x.
fleft(xright)=2^{x}
frac{d}{dx}left(2^{x}right)
Notice that the line for the derivative (the one that has the d/dx) is below the original function.
2. Same thing but with 5^x
fleft(xright)=5^{x}
frac{d}{dx}left(5^{x}right)
Now you’ll notice the derivative line is above the original function.
3. Now with e
fleft(xright)=e^{x}
frac{d}{dx}left(e^{x}right)
These two lines are on top of each other.
Hope that helps make more sense of it. From one layman to another
Latest Answers