let's try to approximate e^x f(x) is equal to e^x and what makes this really simple is when you take the derivative and frankly this is one of the amazing things about the number e is that when you take the derivative of e^x, you get e^x so this is equal to f ' (x) this is equal to f 2nd derivative of x this is equal to f 3rd derivative of x this is equal to the nth derivative of x it's always equal to e^x that's the first mind-blowing thing about e you can just keep taking it's derivative the slope at any point on that curve is the same as the value of the point on that curve that's kind of crazy with that said