Economics









CONTINUITY AND DIFFERENTIABILITY

The derivative of logx. w.r.t. x is. 1 x. ; i.e.. 1. (log ) d x dx x. = . 5.1.12 Logarithmic differentiation is a powerful technique to differentiate 
leep


Dimensions of Logarithmic Quantities

to imply that log (x) is itself dimensionless whatever the dimensions of x. Differentiating eq 5 with respect to temperature gives.


New sharp bounds for the logarithmic function

5 mar. 2019 In this paper we present new sharp bounds for log(1 + x). We prove ... and


Compiled & Conducted @ JKSC

d (log x) = 1 dx x d (ex ) = ex dx d (ax) = ax.loga dx d (sin x) = cos x dx d (cos x) = ans : dy = x + 3 + (2x + 3). log x ... Differentiating wrt x ;.
MATH CH DIFFERENTIATION OTHER COLLEGE





Chapter 8 Logarithms and Exponentials: logx and e

x. = d dx log x. Then log xy and log x have the same derivative from which it follows by the Corollary to the Mean Value Theorem that these two functions 
chapter


Appendix: algebra and calculus basics

28 sept. 2005 6. The derivative of the logarithm d(log x)/dx
algnotes


DIFFERENTIAL EQUATIONS

An equation involving derivative (derivatives) of the dependent variable with Now substituting x = 1 in the above
leep


University of Plymouth

25 mai 2005 For the second part x2 is treated as a constant and the derivative of y3 with respect to y is 3y2. Exercise 1. Find. ∂z. ∂x and. ∂z. ∂ ...
PlymouthUniversity MathsandStats partial differentiation





Economics

Differentiation is all about measuring x x y y. −. − gives slope of the line connecting 2 points (x1 ... NOTE: the derivative of a natural log.
topic


RS Aggarwal Solutions Class 12 Maths Chapter 10 - Differentiation

RS Aggarwal Solutions for Class 12 Maths Chapter 10 -. Differentiation. 4. (i) tan (logx). (ii) log sec x. (iii) log sin x/2. Solution: 
RS Aggarwal Solutions Class Maths Chapter Differentiation


213448 Economics 1

Topic 6: Differentiation

Jacques Text Book (edition 4 ):

Chapter 4

1.Rules of Differentiation

2.Applications

2

Differentiation is all about measuring

change!

Measuring change in a linear function:

y = a + bx a= intercept b= constant slope i.e. the impact of a unit change in x on the level of y b= = xy 1212
xxyy 3

If the function is non-linear:

e.g. if y = x 2

010203040

0123456

X y=x2 xy 1212
xxyy gives slope of the line connecting 2 points (x 1 , y 1 ) and (x 2 ,y 2 ) on a curve (2,4) to (4,16): slope = (16-4) (4-2) = 6 (2,4) to (6,36): slope = (36-4) 6-2 = 8 4

The slope of a curve is equal to the slope of

the line (or tangent) that touches the curve at that point

Total Cost Curve

0510152025303540

1234567

X y=x2 which is different for different values of x 5

Example:A firms cost function is

Y = X 2

X X Y Y

0 1 2 3 4 +1 +1 +1 +1 0 1 4 9 16 +1 +3 +5 +7 Y = X 2

Y+Y = (X+X)

2

Y+Y =X

2 +2X.X+X 2

Y = X

2 +2X.X+X 2 - Y since Y = X 2

Y = 2X.X+X

2 X Y = 2X+X

The slope depends on X and X

6

The slope of the graph of a function

is called the derivative of the function • The process of differentiation involves letting the change in x become arbitrarily small, i.e. letting x 0 • e.g if = 2X+X and X 0 •= 2X in the limit as X 0 xy dxdyxf x o'0 lim)(' 7 the slope of the non-linear function Y = X 2 is 2X •the slope tells us the change in y that results from a very small change in X •We see the slope varies with X e.g. the curve at X = 2 has a slope = 4 and the curve at X = 4 has a slope = 8 •In this example, the slope is steeper at higher values of X 8

Rules for Differentiation

(section 4.3)

1. The Constant Rule

1

Topic 6: Differentiation

Jacques Text Book (edition 4 ):

Chapter 4

1.Rules of Differentiation

2.Applications

2

Differentiation is all about measuring

change!

Measuring change in a linear function:

y = a + bx a= intercept b= constant slope i.e. the impact of a unit change in x on the level of y b= = xy 1212
xxyy 3

If the function is non-linear:

e.g. if y = x 2

010203040

0123456

X y=x2 xy 1212
xxyy gives slope of the line connecting 2 points (x 1 , y 1 ) and (x 2 ,y 2 ) on a curve (2,4) to (4,16): slope = (16-4) (4-2) = 6 (2,4) to (6,36): slope = (36-4) 6-2 = 8 4

The slope of a curve is equal to the slope of

the line (or tangent) that touches the curve at that point

Total Cost Curve

0510152025303540

1234567

X y=x2 which is different for different values of x 5

Example:A firms cost function is

Y = X 2

X X Y Y

0 1 2 3 4 +1 +1 +1 +1 0 1 4 9 16 +1 +3 +5 +7 Y = X 2

Y+Y = (X+X)

2

Y+Y =X

2 +2X.X+X 2

Y = X

2 +2X.X+X 2 - Y since Y = X 2

Y = 2X.X+X

2 X Y = 2X+X

The slope depends on X and X

6

The slope of the graph of a function

is called the derivative of the function • The process of differentiation involves letting the change in x become arbitrarily small, i.e. letting x 0 • e.g if = 2X+X and X 0 •= 2X in the limit as X 0 xy dxdyxf x o'0 lim)(' 7 the slope of the non-linear function Y = X 2 is 2X •the slope tells us the change in y that results from a very small change in X •We see the slope varies with X e.g. the curve at X = 2 has a slope = 4 and the curve at X = 4 has a slope = 8 •In this example, the slope is steeper at higher values of X 8

Rules for Differentiation

(section 4.3)

1. The Constant Rule


12345 Next
  1. log x differentiation formula
  2. log x differentiation by first principle
  3. log x differentiate
  4. log x derivative
  5. log x derivative by first principle
  6. log x derivative formula
  7. log x derivative proof
  8. log 1/x differentiation