3.8: Derivatives of inverse trig functions

Slides:

Advertisements

Similar presentations

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric.

Advertisements

Quiz TUESDAY 3.1, 3.2 Find derivatives using original and alternate definition of the derivative Understanding the definition of derivative (examples 2.

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(

Equations of Tangent Lines

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

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.

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.

What is entry A in the matrix multiplication: ( a) 1 (b) -2(c) 5 (d) 11(e) 13 (f) 0.

Differentiating the Inverse. Objectives Students will be able to Calculate the inverse of a function. Determine if a function has an inverse. Differentiate.

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

We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:

The Chain Rule Section 2.4.

Sec 3.2: The Derivative as a Function If ƒ’(a) exists, we say that ƒ is differentiable at a. (has a derivative at a) DEFINITION.

2.4 Chain Rule. Chain Rule If y=f(u) is a differentiable function of u and u=g(x) is a differentiable function of x then y=f(g(x)) is a differentiable.

3.9: Derivatives of Exponential and Log Functions Objective: To find and apply the derivatives of exponential and logarithmic functions.

Chapter 4 Identities 4.1 Fundamental Identities and Their Use

Lesson: Derivative Techniques 2  Obj - Derivatives of Trig Functions.

 3.8 Derivatives of Inverse Trigonometric Functions.

Derivatives of Inverse Trigonometric Functions

Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 

We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:

2.3 The Product and Quotient Rules and Higher Order Derivatives

{ Chapter 4 Practice AP Calculus. Differentiate:

4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.

HIGHER ORDER DERIVATIVES Product & Quotient Rule.

Section 3.1 – The Inverse Sine, Cosine and Tangent Functions Continued.

3.8 Derivatives of Inverse Trigonometric Functions What you’ll learn about… Derivatives of Inverse Functions Why? The relationship between the graph of.

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:

WARM UP: h(x)=f(g(x)). Identify f(x) and g(x). 1. h(x)=sin(2x) 2. h(x)=(x 2 +2) 1\2 3. If h(x)=f(g(j(x))), identify f(x), g(x) and j(x): h(x)=cos 2 (sinx)

Some needed trig identities: Trig Derivatives Graph y 1 = sin x and y 2 = nderiv (sin x) What do you notice?

Unit 5C Day 2. Do Now  Let y = arccosu. Then u = ______.  Use this to derive dy / dx [arccosu].

Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

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

Math 1411 Chapter 2: Differentiation 2.3 Product and Quotient Rules and Higher-Order Derivatives.

Section 3.8. Derivatives of Inverse Functions Theorem: If is differentiable at every point of an interval I and is never zero on I, then has an inverse.

Section 3.9 Linear Approximation and the Derivative.

3.5: Derivatives of Trig Functions Objective: Students will be able to find and apply the derivative of a trigonometric function.

UNIT 2 LESSON 9 IMPLICIT DIFFERENTIATION 1. 2 So far, we have been differentiating expressions of the form y = f(x), where y is written explicitly in.

Derivatives of Inverse Trigonometric Functions. Integrals.

Inverse Trigonometric Functions: Differentiation & Integration (5. 6/5

Find the values of the six trigonometric functions for 300

Inverse trigonometric functions and their derivatives

Chapter 5 Review JEOPARDY -AP Calculus-.

4-3 inviting inverses of trig deriv’s

Chapter 3 Derivatives.

Warm Up Determine the average rate of change of

Implicit Differentiation

DIFFERENTIATION RULES.

Derivatives of Inverse Trig Functions

Derivatives-Second Part

Warm-Up: November 3, 2017 Find

47 – Derivatives of Trigonometric Functions No Calculator

Derivatives of Inverse Trigonometric Functions

The Derivative and the Tangent Line Problems

Solve the equation for x. {image}

Derivatives of Trig Functions

Derivatives of Inverse Trig Functions

9.1 Identities and Proofs Identify possible identities by using graphs

Differentiate. f (x) = x 3e x

A graphing calculator is required for some problems or parts of problems 2000.

The Chain Rule Section 3.4.

Inverse Trig Functions

Derivatives of Inverse Trigonometric Functions

8. Derivatives of Inverse and Inverse Trig Functions

19. More Solving Equations

5.2(c) Notes: A Bit of Calculus in Verifying Trig Identities

The Chain Rule Section 2.4.

More with Rules for Differentiation

Lesson: Derivative Techniques 2

Presentation transcript:

3.8: Derivatives of inverse trig functions Objective: Students will be able to… Find the derivative of inverse functions and inverse trig functions

Is sec x one to one?

Proof: y= sec (x) Write inverse: Differentiate:

If u is a differentiable function, then,

Examples: find the derivative

Derivative of the other three Inverse Function—Inverse Cofunction Identities

Therefore,

Examples:

Find an equation for the tangent line to the graph y=cot-1x at x = 1.

Calculator conversion identities