chapter 2 2.4 continuity chapter 3 3.1 derivatives of polynomials and exponential functions
TRANSCRIPT
CHAPTER 2 2.4 Continuity
CHAPTER 3
3.1 Derivatives of Polynomials and Exponential Functions
CHAPTER 2 2.4 Continuity
Derivative of a Constant Function
(d/dx) (c) = 0
(d /dx) (x) = 1
The Power Rule If n is a positive integer, then
(d /dx) (x n) = n xn-1
CHAPTER 2 2.4 Continuity
Example Find the derivatives of the given functions.
a)f(x) = 3x4 + 5
b)g(x) = x3 + 2x + 9
CHAPTER 2 2.4 Continuity
The Power Rule (General Rule) If n is any real number, then
(x n)’ = n xn-1
The Constant Multiple Rule If c is a constant and f is a differentiable function, then
[ c f(x) ]’= c f’(x)
CHAPTER 2 2.4 Continuity
Example Find the derivatives of the given functions.
a) f(x)= -3x4
b)f(x) = x .___
CHAPTER 2 2.4 Continuity
The Sum Rule If f and g are both differentiable, then [ f(x) + g(x)]’ = f’(x) + g’(x)
The Difference Rule If f and g are both differentiable, then [ f(x) - g(x)]’ = f’(x) – g’(x)
CHAPTER 2 2.4 Continuity
Example Find the derivatives of the given functions.
a) y = (x2 – 3) / x
b) f(x) = x2 _ 7x + 55.
CHAPTER 2 2.4 Continuity
Definition of the Number e
e is the number such that
lim h 0 (eh – 1) / h = 1.
Derivative of the Natural Exponential Function
( ex )’ = ex .
CHAPTER 2 2.4 Continuity
Example Differentiate the functions:
a) y = x2 + 2 ex
b) y = e x+1 + 1.