OK – The shortcuts!! Thank goodness – i thought she was going to make me do it all the definition way which is such a pain in the a** - why did i have.

Slides:

Advertisements

Similar presentations

Complex Functions These derivatives involve embedded composite, product, and quotient rules. The functions f or g must be derived using another rule.

Advertisements

U2 L8 Chain and Quotient Rule CHAIN & QUOTIENT RULE

The Chain Rule Section 3.6c.

Equations of Tangent Lines

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

1.4 – Differentiation Using Limits of Difference Quotients

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

Section 2.3: Product and Quotient Rule. Objective: Students will be able to use the product and quotient rule to take the derivative of differentiable.

Simplifying Fractions. October 1, 2012 Standard: 6.NS.1. Interpret & compute quotients of fractions, & solve word problems involving division of fractions.

Copyright©amberpasillas2010. Simplify two different ways. == = =

How can one use the derivative to find the location of any horizontal tangent lines? How can one use the derivative to write an equation of a tangent line.

2.3 More on Laws of Exponents. 2.3 Objectives O To model behavior of exponents using function machines O To understand and apply the quotient laws of.

Differentiation Formulas

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

3.3: Rules of Differentiation Objective: Students will be able to… Apply the Power Rule, Sum and Difference Rule, Quotient and Product Rule for differentiation.

Implicit Differentiation 3.6. Implicit Differentiation So far, all the equations and functions we looked at were all stated explicitly in terms of one.

Rational Expressions and Equations Chapter 6. § 6.1 Simplifying, Multiplying, and Dividing.

Exponents. Review: Evaluate each expression: 1.3 ³ 2.7¹ 3.-6² 4.(⅜)³ 5.(-6)² 6.3· 2³ Answers /

1.6 – Tangent Lines and Slopes Slope of Secant Line Slope of Tangent Line Equation of Tangent Line Equation of Normal Line Slope of Tangent =

Tangents. The slope of the secant line is given by The tangent line’s slope at point a is given by ax.

Chapter 3.1 Tangents and the Derivative at a Point.

Multiplying Fractions & Mixed Numbers RULES: 1. Change all mixed and whole numbers to improper. 2. Cross cancel (short cut). 3. Multiply numerators and.

3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)

Powerpoint Templates Page 1 Powerpoint Templates Review Calculus.

Quotient Rule Finding the derivative of a function using the Quotient Rule Andrew Conway.

Derivatives Using the Limit Definition

Aim: How do we find the derivative by limit process? Do Now: Find the slope of the secant line in terms of x and h. y x (x, f(x)) (x + h, f(x + h)) h.

Chain Rule 3.5. Consider: These can all be thought of as composite functions F(g(x)) Derivatives of Composite functions are found using the chain rule.

position time position time tangent!  Derivatives are the slope of a function at a point  Slope of x vs. t  velocity - describes how position changes.

Clicker Question 1 What is the derivative function f '(x ) of the function ? (Hint: Algebra first, calculus second!) A. 12x 2 – (5/2)x -1/2 B. 12x 2 –

More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x 2 – 4x 4 +1.

2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.

The Derivative Calculus. At last. (c. 5). POD Review each other’s answers for c. 4: 23, 25, and 27.

Derivative Shortcuts -Power Rule -Product Rule -Quotient Rule -Chain Rule.

After the test… No calculator 3. Given the function defined by for a) State whether the function is even or odd. Justify. b) Find f’(x) c) Write an equation.

4.2:DERIVATIVES OF PRODUCTS AND QUOTIENTS Objectives: To use and apply the product and quotient rule for differentiation.

Exponents. Review: Evaluate each expression: 1.3 ³ 2.7¹ 3.-6² 4.(⅜)³ 5.(-6)² 6.3· 2³ Answers /

Basic Rules of Derivatives Examples with Communicators Calculus.

2.3 Basic Differentiation Formulas

DIFFERENCE QUOTIENT, DERIVATIVE RULES, AND TANGENT LINES RIZZI – CALC BC.

Shortcuts for Derivatives

§ 4.2 The Exponential Function e x.

Mean Value Theorem.

Rules for Differentiation

3-3 rules for differentiation

MTH1150 Tangents and Their Slopes

§ 1.3 The Derivative.

Implicit Differentiation

Used for composite functions

The Quotient Rule The Quotient Rule is used to find derivatives for functions written as a fraction:

3.1 Polynomial & Exponential Derivatives

2.3 Basic Differentiation Formulas

Slope at Point of Tangency

Sec 2.7: Derivative and Rates of Change

Definition of the Derivative

The Derivative and the Tangent Line Problems

Derivatives by Definition

2.4 The Chain Rule.

Multiplying and Dividing Rational Expressions

Exam2: Differentiation

(This is the slope of our tangent line…)

The Product & Quotient Rules

Exam2: Differentiation

MATH 1314 Lesson 6: Derivatives.

The Chain Rule Section 3.6b.

Differentiation Using Limits of Difference Quotients

More with Rules for Differentiation

Presentation transcript:

OK – The shortcuts!! Thank goodness – i thought she was going to make me do it all the definition way which is such a pain in the a** - why did i have to do it the long way anyway? I deserve the shortcut. I don’t need to earn it – i am owed by divine right. i’m also hungry. I should have eaten more at lunch. Wonder if I could pretend I have to go to the bathroom.. And go down to the bookstore and get chocolate…mmmmm chocolate

4. Product Rule 5.Quotient Rule 6. Generalized Power Rule

Derivation of Power Rule n terms

Derivation of Product Rule

Examples

Hints on Quotients 1.See if the fraction simplifies first. is harder as is. If you factor and cancel it makes the problem MUCH easier. 2.Share a simple denominator. isn’t as easy to simplify as

Equation of Tangent line What do you need for the equation of a tangent line? You need 1) slope 2) point This is an easy problem with short cut derivatives.

How will we get the slope? By definition the derivative is the slope of a curve. So, you will take the derivative of the function and plug x (and maybe y) into the function to get the slope.

How will we get the point? Usually given to you. How easy. Find the equation of the line tangent to f(x) at the point (4, 1) if

Example