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8.6.4 The 0 = xD Operator This operator consists of first taking the derivative of a function and then multiplying by x, i.e., Of (x) = (xD)f(x) = xF(x) dx (8.234) Therefore, Co*s(2) = #(@{(x}) = 0 df (x) d df (x) = x- dx dx dx df (x) + x2. 2 d² f (x) (xD+a² D²)f(x), = x dx (8.235) %3D dx² and f(x) = (xD+3x² D² + æ³ D³)ƒ(x). (8.236) In general, we have On f(x) = (8.237)

8.6.4 The 0 = xD Operator This operator consists of first taking the derivative of a function and then multiplying by x, i.e., Of (x) = (xD)f(x) = xF(x) dx (8.234) Therefore, Co*s(2) = #(@{(x}) = 0 df (x) d df (x) = x- dx dx dx df (x) + x2. 2 d² f (x) (xD+a² D²)f(x), = x dx (8.235) %3D dx² and f(x) = (xD+3x² D² + æ³ D³)ƒ(x). (8.236) In general, we have On f(x) = (8.237)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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+ 72 = xD Operator 8.6.4 The 0 This operator consists of first taking the derivative of a function and then multiplying by x, i.e., df (x) Of (x) = (xD)f(x) = x- dx (8.234) Therefore, (6° f(2) = 0(0f(x)) = 0 df (x) d df (x) = x: dx %3D dx dx df (x) „2d² f(x) (xD+ a² D²)f (x), (8.235) dx dx2 and C0 (xD+3x² D° + a°D³)ƒ(x). *f (x) = (8.236) In general, we have n O" f(x) = Cm D", (8.237) т-1 where the C can be calculated. (See for example, Jordan 1979, Section 69.) Note that if f(x) is a polynomial function of degree p, then OP f (x) is also of degree p. The following special cases illustrate the consequences of applying the 0 operator: (i) d A = 0. dx A = constant, 0A = (8.238) (ii) Өх — х. (8.239) (iii) qx", (8.240a) o² xª = q²x? (8.240b) (8.240c) q"x9. (iv) (*) d In x = x. O In x (8.241) dx (v) If Pm(x) = E, a;x*, then т. 0" Pm (x) = a;i"x'. (8.242) i=0
Transcribed Image Text:+ 72 = xD Operator 8.6.4 The 0 This operator consists of first taking the derivative of a function and then multiplying by x, i.e., df (x) Of (x) = (xD)f(x) = x- dx (8.234) Therefore, (6° f(2) = 0(0f(x)) = 0 df (x) d df (x) = x: dx %3D dx dx df (x) „2d² f(x) (xD+ a² D²)f (x), (8.235) dx dx2 and C0 (xD+3x² D° + a°D³)ƒ(x). *f (x) = (8.236) In general, we have n O" f(x) = Cm D", (8.237) т-1 where the C can be calculated. (See for example, Jordan 1979, Section 69.) Note that if f(x) is a polynomial function of degree p, then OP f (x) is also of degree p. The following special cases illustrate the consequences of applying the 0 operator: (i) d A = 0. dx A = constant, 0A = (8.238) (ii) Өх — х. (8.239) (iii) qx", (8.240a) o² xª = q²x? (8.240b) (8.240c) q"x9. (iv) (*) d In x = x. O In x (8.241) dx (v) If Pm(x) = E, a;x*, then т. 0" Pm (x) = a;i"x'. (8.242) i=0
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