Lecture Note
University
Rice UniversityCourse
Preparing for the AP Calculus AB ExamPages
1
Academic year
2022
Awayne
Views
60
p {margin: 0; padding: 0;} .ft00{font-size:19px;font-family:CourierNew;color:#000000;} .ft01{font-size:16px;font-family:CourierNew;color:#000000;} .ft02{font-size:16px;line-height:18px;font-family:CourierNew;color:#000000;} Higher Order Derivatives Now, we've been saying "first derivative" so much. And you can'thave a first without a second, or a third, or even a fourth. So there really is no limit – pun intended – to how many derivativesa function can have. You probably already knew they were coming, because we've always had "first derivative." And if you have afirst derivative," it's likely that you're going to have a secondderivative too." Notationally, we call the derivative of some function f(x) "f-prime".In finding the derivative of f(x), we usually call it f'(x). Therereally is no limit to what you do. You could go f''(x) if youwanted to, or even f'''(x). At some point, though, it gets a little tedious to keep writing primes over and over and overagain.We'll write f to the n, where n is the derivative number--derivatives taken of x. So take the 20th derivative, we'll there you'd go.It'd be f 20 of x. This is the Newton notation.The Leibniz notation is often used to represent the secondderivative of a function, where f'(x) stands for the first derivative of function f(x).
Higher Order Derivatives
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