04Higher Derivatives

# 04Higher Derivatives - After the third derivative, we...

This preview shows pages 1–2. Sign up to view the full content.

H IGHER D ERIVATIVES Finding higher derivatives (second, third, fourth, etc. derivatives) of a function is the same method as finding the first derivative. ) ( ) ( ) ( 2 2 2 2 x f D x f D dx y d dx dy dx d x f y x = = = = = The first derivative can be interpreted as the slope of the tangent line, and the second derivative can be interpreted as the rate of change of the slope of the tangent line (more when we get to curve sketching). We can also define higher derivatives: the third derivative is the derivative of the second derivative. We write it as ) ( ) ( 3 3 3 3 ) 3 ( x f D x f D dx y d y f f x x = = = = = . To find the second derivative, find the first derivative and differentiate that.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: After the third derivative, we don’t use prime notation. In general, the th n derivative of f is denoted by ) ( ) ( ) ( x f D x f D x y d x y f n x n n n n n = = = = . Ex . Find the first five derivatives of 6 3 5 2 2 3 4-+-+ = x x x x y . Ex . Find the third derivative of 3 1 x y = . Hints to Derivatives: 1. Learn the Rules. 2. Simplify function – change radicals to fractional exponents and collect like terms. Assign: p. 198 #45-50, Higher Derivatives Worksheet (no implicit differentiation)...
View Full Document

## This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

### Page1 / 2

04Higher Derivatives - After the third derivative, we...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online