Section 4.4 The Chain Rule No ln x 3.3.

Slides:



Advertisements
Similar presentations
Section 7.6 – Numerical Integration
Advertisements

Inflection Points and the Second Derivative
AP Exam The Final Hours of Test Prep…. Tonight Dont cram – youve spent a month studying for this exam! Spend a little time reviewing –Practice tests –FRQs.
When you see… Find the zeros You think…. To find the zeros...
Unit 6 – Fundamentals of Calculus Section 6
The Chain Rule Section 3.6c.
Section 2.6 Slopes of tangents  SWBAT:  Find slopes of tangent lines  Calculate velocities.
Section 2.2 Instantaneous Rates of Change
Meanings of the Derivatives. I. The Derivative at the Point as the Slope of the Tangent to the Graph of the Function at the Point.
Section 4.4 The Chain Rule. Find f ‘ (x) if Try these two…
Section 4.4 The Chain Rule No ln x 3.3. Easiest explained using examples.
Calculus Review - Calculator 1. Let h(x) be the anti- derivative of g(x). If - 1.
Concavity & the second derivative test (3.4) December 4th, 2012.
Rates of Change and Tangent Lines Section 2.4. Average Rates of Change The average rate of change of a quantity over a period of time is the amount of.
Find the numerical value of the expression. sinh ( ln 4 )
Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.
3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.
Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.
Section Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.
M 112 Short Course in Calculus Chapter 2 – Rate of Change: The Derivative Sections 2.2 – The Derivative Function V. J. Motto.
Warm Up 10/3/13 1) The graph of the derivative of f, f ’, is given. Which of the following statements is true about f? (A) f is decreasing for -1 < x
Section 4.2 – Differentiating Exponential Functions Section 4.3 – Product Rule/Quotient Rule THE MEMORIZATION LIST BEGINS.
1 When you see… Find the zeros You think…. 2 To find the zeros...
Section 4.2 – Differentiating Exponential Functions THE MEMORIZATION LIST BEGINS.
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.
Velocity and Other Rates of Change Notes: DERIVATIVES.
Exponential and Log Derivatives
Basic Differentiation Rules
A1 – Rates of Change IB Math HL&SL - Santowski. (A) Average Rates of Change Use graphing technology for this investigation (Winplot/Winstat/GDC) PURPOSE.
AP Calculus AB Exam 3 Multiple Choice Section Name:_____________ 2. An equation of the line tangent to the graph of f( x ) = x ( 1 – 2x) 3 at the point.
Section 5.5 The Intermediate Value Theorem Rolle’s Theorem The Mean Value Theorem 3.6.
Derivatives Test Review Calculus. What is the limit equation used to calculate the derivative of a function?
Review Problems Integration 1. Find the instantaneous rate of change of the function at x = -2 _ 1.
1 When you see… Find the zeros You think…. 2 To find the zeros...
Implicit differentiation (2.5) October 29th, 2012.
Section 7.6 – Numerical Integration. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.
Section 7.6 – Numerical Integration. represents the area between the curve 3/x and the x-axis from x = 4 to x = 8.
1.1 Preview to calculus. Tangent line problem Goal: find slope of tangent line at P Can approximate using secant line First, let Second, find slope of.
Section Continuity 2.2.
Section 3.8 Higher Derivatives AP Calculus October 7, 2009 Berkley High School, D2B2
When you see… Find the zeros You think…. To find the zeros...
Section 2.1 – Average and Instantaneous Velocity.
Section 2.4 Rates of Change and Tangent Lines Calculus.
§ 4.2 The Exponential Function e x.
When you see… Find the zeros You think….
Business Mathematics MTH-367
47 – Derivatives of Trigonometric Functions No Calculator
Section 3.2 – Calculating Areas; Riemann Sums
The Fundamental Theorem of Calculus Part 1 & 2
When you see… Find the zeros You think….
When you see… Find the zeros You think….
3.1 Section 2.2 Average and Instantaneous Rate of Change
2.2C Derivative as a Rate of Change
Section 11.3 Euler’s Method
Product Rule/Quotient Rule
Continuity and Differentiation
Find the derivative Find the derivative at the following point.
Section 3.2 Calculus AP/Dual, Revised ©2017
Chapter 3 Derivatives.
Derivative Practice Family of f: f & f’ & f’’ Definition Of the
Concavity of a Function
Section 3.2 – Calculating Areas; Riemann Sums
Ordered pairs: ( , ) ( , ) ( , ) Ordered pairs: ( , ) ( , ) ( , )
Warm-Up!
The Chain Rule Section 3.4.
Concavity of a Function
Product Rule/Quotient Rule
The Chain Rule Section 3.6b.
Concavity of a Function
The Chain Rule Section 2.4.
Presentation transcript:

Section 4.4 The Chain Rule No ln x 3.3

Easiest explained using examples

Find f ‘ (x) if Find f ‘ (x) if

NO CALCULATOR

NO CALCULATOR OPTION A OPTION B

NO CALCULATOR

NO CALCULATOR What is the instantaneous rate of change at x = 0 of the function f given by

NO CALCULATOR The y-intercept of the tangent line to the curve

NO CALCULATOR

CALCULATOR REQUIRED The slope of the curve at its point of inflection is

NO CALCULATOR

NO CALCULATOR

CALCULATOR REQUIRED Let the function f be differentiable on the interval [0, 2.5] and Use the table to estimate g ‘ (1) if

CALCULATOR REQUIRED The position of a particle moving on the x-axis, starting at t = 0, is given by Which of the following statements is true? The particle is at a positive position on the x-axis at time t = (a + b)/2 The particle is at rest at time t = a The particle is moving to the right at time t = b. NO YES YES A) I only B) II only C) III only D) I and II only E) II and III only

. Fill in the chart below. -2 1 1 2 P. 225 #45 Finish

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR

NO CALCULATOR