3.8 Derivatives of Inverse Functions Fri Oct 30

Slides:

Advertisements

Similar presentations

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

Advertisements

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.

4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.

1.6 Composition of Functions Thurs Sept 18

Derivative of an Inverse AB Free Response 3.

3.9 Exponential and Logarithmic Derivatives Wed Nov 12 Do Now Find the derivatives of: 1) 2)

4.9 Antiderivatives Wed Jan 7 Do Now If f ’(x) = x^2, find f(x)

1 The Product and Quotient Rules and Higher Order Derivatives Section 2.3.

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

Do Now Determine the open intervals over which the following function is increasing, decreasing, or constant. F(x) = | x + 1| + | x – 1| Determine whether.

3.9 Exponential and Logarithmic Derivatives Thurs Oct 8

5.1 Composite Functions Goals 1.Form f(g(x)) = (f  g) (x) 2.Show that 2 Composites are Equal.

Slide 1- 1 Sum, Difference, Product, and Quotient.

6-1: Operations on Functions (Composition of Functions)

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

Section 3.3 The Product and Quotient Rule. Consider the function –What is its derivative? –What if we rewrite it as a product –Now what is the derivative?

AP CALCULUS 1009 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.

3.2 The Power Rule Thurs Oct 22 Do Now Find the derivative of:

Lesson 5.3 Inverse Functions

1 The Chain Rule Section After this lesson, you should be able to: Find the derivative of a composite function using the Chain Rule. Find the derivative.

7-4 Remainder and Factor Theorems. Solve. x 3 + 4x x - 18 = 0 If x - 3 is a factor.

Inverse Trig functions

4.4 The Fundamental Theorem of Calculus. Essential Question: How are the integral & the derivative related?

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

5.3 Fundamental Theorem of Calculus Part 1 Fri Nov 20 Do Now Use geometry to compute the area represented by the integral.

Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x

3.6 Trigonometric Functions Wed Oct 21 Do Now Find the y’’ and y’’’ 1) 2)

3.1 The Derivative Wed Oct 7 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4.

3.9 Exponential and Logarithmic Derivatives Mon Nov 9 Do Now Find the derivatives of: 1) 2)

The Product and Quotient Rules for Differentiation.

3.3 Product Rule Tues Oct 27 Do Now Evaluate each 1) 2)

3-5 Higher Derivatives Tues Oct 20 Do Now Find the velocity at t = 2 for each position function 1) 2)

AP CALCULUS 1008 : Product and Quotient Rules. PRODUCT RULE FOR DERIVATIVES Product Rule: (In Words) ________________________________________________.

2011 – Chain Rule AP CALCULUS. If you can’t do Algebra.... I guarantee you someone will do Algebra on you!

3.8 Derivatives of Inverse Functions Wed Oct 5

Then  a # c in (a, b) such that f  (c) = 0.

Section 3.3 The Product and Quotient Rule

2016 Derivatives of Inverse Trig Functions

Find the derivative Find the second derivative

Learning Target: I will determine if a function is increasing or decreasing and find extrema using the first derivative. Section 3: Increasing & Decreasing.

Derivative of an Exponential

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

Chain Rule AP Calculus.

Fall Break Chain Rule Review

2.4 The Chain Rule Use the Chain Rule to find derivative of a composite function. Use the General Power Rule to find derivative of a function. Simplify.

Derivatives of Inverse Functions

3.11: Derivatives of Inverse Functions

The Chain Rule Section 4 Notes.

Differentiation Given the information about differentiable functions f(x) and g(x), determine the value.

5.3 The Derivative of an Inverse Function

Inverse Functions Rita Korsunsky.

Combinations of Functions:

The Derivative of an Inverse Function

Derivatives of Inverse Functions

1.2 Analyzing Graphs of Functions and Relations

6-1: Operations on Functions (+ – x ÷)

Derivatives of Inverse Trig Functions

Warmup 1. What is the interval [a, b] where Rolle’s Theorem is applicable? 2. What is/are the c-values? [-3, 3]

Today in Calculus Go over homework Trig Review Mean Value Theorem

Find the derivative of the following function: {image} .

Lesson 3-8: Derivatives of Inverse Trig Functions

Determine if 2 Functions are Inverses by Compositions

Warm Up Determine the domain of f(g(x)). f(x) = g(x) =

8. Derivatives of Inverse and Inverse Trig Functions

Use Inverse Functions Notes 6.4.

Use Inverse Functions Notes 7.5 (Day 2).

Replace inside with “x” of other function

Concavity & the 2nd Derivative Test

Presentation transcript:

3.8 Derivatives of Inverse Functions Fri Oct 30 Do Now Find the inverse of each function 1) Y = 3x - 5 2) Y = x^4 + 10

HW Review: p.175 #1-85

Derivative of the Inverse Assume f(x) is differentiable and And if f’(g(x)) is not 0 then

Inverse Derivatives We can use the previous theorem to find the derivative of an inverse We can also find the inverse first and differentiate directly

Ex 2 Calculate g’(1) where g(x) is the inverse of f(x) = x + e^x

Inverse Trig Derivatives One of these six might appear on the AP exam:

Closure Calculate where x = 0 HW: p.181 #1-35 odds

DO NOW Find the derivative