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

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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.
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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)...
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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.

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

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