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Example (1) Find the derivative of f(x) = 4 at any point x
Example (2) Find the derivative of f(x) = 4x at any point x
Example (3) Find the derivative of f(x) = x 2 at any point x
Example (4) Find the derivative of f(x) = x 3 at any point x
Example (5) Find the derivative of f(x) = x 4 at any point x
Power Rule Let: f(x) = x n, where n is a real number other than zero Then: f'(x ) = n x n-1 If f(x) = constant, then f ' (x) = 0
Algebra of Derivatives
The Chain Rule The derivative of composite function for the case f(x) = g n (x) Let: f(x) = g n (x) Then: f ' (x) = ng n-1 (x). g ' (x) Example: Let f(x) = (3x 8 - 5x + 3 ) 20 Then f(x) = 20 (3x 8 - 5x + 3 ) 19 (24x 7 - 5)
2.4 The Chain Rule If f and g are both differentiable and F is the composite function defined by F(x)=f(g(x)), then F is differentiable and F′ is given.
Rules for Differentiating Univariate Functions Given a univariate function that is both continuous and smooth throughout, it is possible to determine its.
Zeros of Polynomial Functions Section 2.5. Objectives Use the Factor Theorem to show that x-c is a factor a polynomial. Find all real zeros of a polynomial.
CHAPTER Continuity CHAPTER Derivatives of Polynomials and Exponential Functions.
2.5 Zeros of Polynomial Functions
The Derivative. Definition Example (1) Find the derivative of f(x) = 4 at any point x.
FUNCTIONS : Domain values When combining functions using the composite rules, it is necessary to check the domain for values that could be restricted.
Academy Algebra II/Trig 5.5: The Real Zeros of a Polynomial Functions HW: p.387 (14, 27, 30, 31, 37, 38, 46, 51)
Derivatives of Exponential Functions Lesson 4.4. An Interesting Function Consider the function y = a x Let a = 2 Graph the function and it's derivative.
Section 5.4a FUNDAMENTAL THEOREM OF CALCULUS. Deriving the Theorem Let Apply the definition of the derivative: Rule for Integrals!
4.4c 2nd Fundamental Theorem of Calculus. Second Fundamental Theorem: 1. Derivative of an integral.
Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.
Section 4.3 Zeros of Polynomials. Approximate the Zeros.
Real Zeros of Polynomial Functions 2-3. Descarte’s Rule of Signs Suppose that f(x) is a polynomial and the constant term is not zero ◦The number of positive.
Objectives: 1.Be able to find the derivative using the Constant Rule. 2.Be able to find the derivative using the Power Rule. 3.Be able to find the derivative.
In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
Section 3.4 The Chain Rule. Consider the function –We can “decompose” this function into two functions we know how to take the derivative of –For example.
OPERATIONS WITH DERIVATIVES. The derivative of a constant times a function Justification.
Examples A: Derivatives Involving Algebraic Functions.
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