calculus of exponential and logarithmic...
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![Page 1: Calculus of Exponential and Logarithmic Functionsholyspiritmath3208.weebly.com/uploads/3/8/6/9/38690503/lesson_7.… · Section 7.1 Natural Exp and Log Functions 1 CHAPTER 7 Calculus](https://reader033.vdocuments.net/reader033/viewer/2022043012/5faaaacc7ef59c31f44b18da/html5/thumbnails/1.jpg)
Section 7.1 Natural Exp and Log Functions
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CHAPTER 7
Calculus of Exponential and Logarithmic Functions
(ii)
(iii) Inverse Functions and
(iv) Derivatives of
(v) Logarithmic Differentiation
(vi) Proofs
(i) The number e Euler's number
and
Evaluate
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Exponential and Logarithmic Functions
Inverse Function
What is the inverse of the exponential function ?
X Y X Y
Rule:
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What is the value of e?
irrational number
By letting h take on larger and larger values, the value is close to the decimal value for e.
Exponential and Logarithmic Functions
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Common Logarithms and Natural Logarithms
base 10 base e
Natural logarithm is the inverse of the exponential function
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In order to compute the derivative of the exponential
function , we must first determine the value of the limit
using a table of values.
h
0.01
0.001
0
0.001
0.01
Derivatives
?
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Derivative of
(i) Differentiate
http://www.flashandmath.com/mathlets/calc/derplot/derplot.html
Use definition of limit and the special limit
Technology
Chain Rule:
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Example 1
Determine for the following:
(a)
(b)
(c)
(d)
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(e)
(f)
(g)
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(h)
(i)
(j)
(k)
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Derivative of
Chain Rule: (where u is a function of x)
(i) Differentiate
change to exponential form and use implicit differentiation
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Example 2
Determine for the following:
(b)
(c)
(d)
(a)
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(e)
(f)
(g)
(h)
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(i)
(j)
Simplify the function using the Logarithmic Properties
(k)
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(l)
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