Find {image} by implicit differentiation: {image} .

Slides:

Advertisements

Similar presentations

2.5 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003.

Advertisements

Unit 6 – Fundamentals of Calculus Section 6

The Chain Rule Section 3.6c.

Linear Equations Review. Find the slope and y intercept: y + x = -1.

C1: Tangents and Normals

Equation of a Tangent Line

Point Value : 20 Time limit : 2 min #1 Find. #1 Point Value : 30 Time limit : 2.5 min #2 Find.

Derivative Review Part 1 3.3,3.5,3.6,3.8,3.9. Find the derivative of the function p. 181 #1.

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

Section 2.9 Linear Approximations and Differentials Math 1231: Single-Variable Calculus.

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.

A) Find the velocity of the particle at t=8 seconds. a) Find the position of the particle at t=4 seconds. WARMUP.

Differentiation Jeopardy Power RuleProduct RuleQuotient.

Equations of Tangent Lines April 21 st & 22nd. Tangents to Curves.

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.

1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.

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.

Implicit Differentiation. Implicitly vs. Explicitly Defined Functions y is given explicitly as a function of x (y is solved in terms of x) y is given.

3.7 – Implicit Differentiation An Implicit function is one where the variable “y” can not be easily solved for in terms of only “x”. Examples:

Derivatives Test Review Calculus. What is the limit equation used to calculate the derivative of a function?

Implicit Differentiation Notes 3.7. I. Implicit Form A.) B.) Ex. – C.) Ex. - Find the derivative!

DO NOW: Write each expression as a sum of powers of x:

Calculus and Analytical Geometry

3.8 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003.

The Chain Rule. The Chain Rule Case I z x y t t start with z z is a function of x and y x and y are functions of t Put the appropriate derivatives along.

Chapter 5: Applications of the Derivative Chapter 4: Derivatives Chapter 5: Applications.

DO NOW: Find the inverse of: How do you find the equation of a tangent line? How do you find points where the tangent line is horizontal?

Chapter 9 & 10 Differentiation Learning objectives: 123 DateEvidenceDateEvidenceDateEvidence Understand the term ‘derivative’ and how you can find gradients.

Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd Maximum and minimum points.

Graphing Function Charts. X Y I Y = 2X + 1 X Y ½ Y - intercept 0, 1 X - intercept -½, 0.

Basic Rules of Derivatives Examples with Communicators Calculus.

2.3 Basic Differentiation Formulas

Implicit Differentiation

Implicit Differentiation

3.3: Point-Slope Form.

Implicit Differentiation

Find the equation of the tangent line to the curve y = 1 / x that is parallel to the secant line which runs through the points on the curve with x - coordinates.

3.1 Polynomial & Exponential Derivatives

2.3 Basic Differentiation Formulas

Equations of Tangents.

Differentiating Polynomials & Equations of Tangents & Normals

Implicit Differentiation Continued

Implicit Differentiation

Find the derivative of the vector function r(t) = {image}

The Derivative and the Tangent Line Problems

Differentiate the function. {image}

Find the area of the region enclosed by one loop of the curve. {image}

Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx / dy. y 4 + x 2y 2 + yx 4 = y + 7 {image}

Solve the equation for x. {image}

Polar Coordinates and Polar Graphs

Implicit Differentiation

Literacy in Maths Gradient Tangent Normal

Implicit Differentiation

Solve the differential equation. {image}

Find an equation of the tangent to the curve at the point corresponding to the value of the parameter. {image} {image}

Differentiate. f (x) = x 3e x

Use power series to solve the differential equation. y ' = 7xy

2.5 Implicit Differentiation

2.5 The Chain Rule.

Which equation does the function {image} satisfy ?

Gradients and Tangents

Basic Rules of Differentiation

Find the derivative of the following function: y(x) = -3 sec 9 x.

If {image} choose the graph of f'(x).

1: Slope from Equations Y = 8x – 4 B) y = 6 – 7x

2.5 Basic Differentiation Properties

The figure shows the graphs of {image} , {image} , {image}

Presentation transcript:

Find {image} by implicit differentiation: {image} . 2. 1. none of these {image} 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find {image} by implicit differentiation: {image} 1. 2. {image} none of these 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find an equation of the tangent line to the curve {image} at the point ( 1, 2 ). 1. 2. {image} none of these 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find an equation of the tangent line to the curve {image} at the point (3, 1). 1. 2. {image} None of these 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The curve with equation {image} is called a lemniscate The curve with equation {image} is called a lemniscate. Find the points on the lemniscate at which the tangent is horizontal. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the sum of the x - and y - intercepts of any tangent line to the curve {image} . 8 4 none of these 3 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50