ch07-univariate-calculus

ch07-univariate-calculus - Univariate Calculus Professor...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Univariate Calculus Professor Erkut Ozbay Economics 300
Background image of page 1

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

View Full DocumentRight Arrow Icon
Outline Rules of differentiation Sum rule Scale rule Product rule Power rule Exponential rule Chain rule Quotient rule Logarithmic rule
Background image of page 2
Outline Second derivatives and convexity Economic applications Risk aversion and utility functions Elasticities Total revenue Average, marginal, and total cost
Background image of page 3

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

View Full DocumentRight Arrow Icon
Rules of differentiation Used to evaluate derivative of any function Much easier than working with basic definition 0 ( ) ( ) lim x dy f x x f x dx x ∆ → + ∆ - =
Background image of page 4
Sum rule ( ) ( ) ( ) ( ) ( ) ( ) y h x f x g x dy h x f x g x dx = = + = = +
Background image of page 5

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

View Full DocumentRight Arrow Icon
Scale rule ( ) ( ) ( ) ( ) y h x kf x dy h x kf x dx = = = =
Background image of page 6
Product rule ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) y h x f x g x dy h x f x g x f x g x dx = = = = +
Background image of page 7

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

View Full DocumentRight Arrow Icon
Power rule 1 ( ) ( ) n n y h x kx dy h x nkx dx - = = = =
Background image of page 8
Exponential rule ( ) ( ) kx kx y h x e dy h x ke dx = = = =
Background image of page 9

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

View Full DocumentRight Arrow Icon
Chain rule ( ) ( ( )) ( ) ( ( )) ( ) y h x g f x dy h x g f x f x dx = = = = ( ) ( ) y g u u f x dy dy du dx du dx = = =
Background image of page 10
Quotient rule 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) f x y h x g x dy f x g x f x g x h x dx g x = = - = =
Background image of page 11

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

View Full DocumentRight Arrow Icon
Logarithmic rule ( ) ln 1 ( ) ( ) log 1 1 ( ) ln b y f x x dy f x dx x y f x x dy f x dx x b = = = = = = = =
Background image of page 12
Exercise 3 4 2 2 25 7 4 8 3 14 1 2 3 y x y y x y x x y x x - = = = = + - = - 3 2 dy x dx = 5 7 dy x dx - = - 1/2 3 16 2 dy x x dx - = + 3 2 2 3 dy x dx - = - -
Background image of page 13

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

View Full DocumentRight Arrow Icon
Exercise 2 2 2 4 20 4 3ln 2( 1) x y x x y e y x y x = + - = = = + 20 8 dy x dx = - 2 2 x dy e dx = 3 dy dx x = 4( 1) dy x dx = +
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 43

ch07-univariate-calculus - Univariate Calculus Professor...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online