Warm Up Determine the derivative of each of the following.

Slides:

Advertisements

Similar presentations

Graphs of the Other Trigonometric Functions Section 4.6.

Advertisements

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.

Section 2.4 – The Chain Rule. Example 1 If and, find. COMPOSITION OF FUNCTIONS.

Practice. Graph and find the following (unless it doesn’t apply to that type of graph): amplitude, period, increment, sinusoidal axis, starting.

Tips For Learning Trig Rules. Reciprocal Rules Learn:

Warm Up Sign Up. AccPreCalc Lesson 27 Essential Question: How are trigonometric equations solved? Standards: Prove and apply trigonometric identities.

Warm Up: h(x) is a composite function of f(x) and g(x). Find f(x) and g(x)

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

 Content  What is derivation?  Derivation of trigonometry function  Derivation’s rules.

Example: Later, though, we will meet functions, such as y = x 2 sinx, for which the product rule is the only possible method.

Trig Functions Ms. Roque 11 th Grade Trigonometry Course Next slide.

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

B.1.8 – Derivatives of Primary Trig Functions Calculus - Santowski 12/1/ Calculus - Santowski.

7.1.1 Trig Identities and Uses

 The derivative of a function f(x), denoted f’(x) is the slope of a tangent line to a curve at any given point.  Or the slope of a curve at any given.

Power Rule If H(x) = (3x 7 If H(x) = (3x 7 -4x) 12 /12 3x 7 then H’(x) = (3x 7 - 4x) 11 (21x 6 - 4) When differentiating, the first answer is multiplied.

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.

Do Now:. 4.5 and 4.6: Graphing Trig Functions Function table: When you first started graphing linear functions you may recall having used the following.

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

Trig Functions of Real Numbers

Warm Up Write an equation of the tangent line to the graph of y = 2sinx at the point where x = π/3.

Powerpoint Jeopardy Definition of Derivatives Basic Derivatives Equation of Tangent Line Product & Quotient Rule Chain Rule

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

A Review of Trigonometric Functions

Charles Schwoerer Jonas Brown RULES START PLAYING! START PLAYING!

Dean Bates P derivatives of trig functions.

Clicker Question 1 What is the derivative of f (x ) = 2x sin(x ) ?

Jeopardy Power Rule Product Rule Quotient Rule Trig Functions Object Motion $100 $200 $300 $400 $500 $ $100 $200 $300 $400 $ $500 Final Jeopardy.

Derivatives of Trig Functions Objective: Memorize the derivatives of the six trig functions.

The Product and Quotient Rules for Differentiation.

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

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

BELL-WORK TCAP Bell-Work # What is the cotangent of angle x if sec(x) = 12 5.

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

Power Rule is a corallary to Chain Rule. Power Rule If f(x) = x n then f ' (x) = n x (n-1) Replacing x by g(x) gives.

The Product Rule. Do Now  Find the derivative of f(x) = x(x 2 + 2x – 1).  What is the derivative of sinx? of cosx?

Trigonometric Identity Review. Trigonometry Identities Reciprocal Identities sin θ = cos θ = tan θ = Quotient Identities Tan θ = cot θ =

Ch 6.7 – Graphing Other Trig Functions. y = cscx Period: Domain: Range: Asymptotes: y = 1: y = -1: 2π2π All real numbers except πn, n is an integer All.

Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1.

Jeopardy Simplify Trig expressions Verify Trig Identities Find all Solutions Solutions with multiple angles Solutions with factoring Q $100 Q $200 Q $300.

Math 1304 Calculus I 3.2 – Derivatives of Trigonometric Functions.

Warm Up Determine the average rate of change of

Derivative of f (x) =sin (x)

Section 5.1 Trigonometric Identities

3.6 Trigonometric Functions Tues Sept 27

Derivatives of Trig Functions

C4 Integration.

9.1: Identities and Proofs

Ch 6.7 – Graphing Other Trig Functions

Over what interval(s) is f increasing?

Derivatives of Trig Functions

Derivatives of Trig Functions

MATH 1330 Section 5.1.

Finding a Limit as x c Plug in---Factor/Conjugate.

Derivatives of Trig Functions

Product and Quotient Rules and Higher Order Derivatives

Warm-up: 1) Given sin = ½ and and csc  > 0 can you find the angle measure  definitively? Given cosx = − And sinx < 0 find the other five trigonometric.

Pythagorean Identities

Pyrhagorean Identities

Last time… Homework questions?.

8.1: Graphical Solutions of Trig Functions

Trig. equations with graphs

Graphing Other Trig. Functions

Lake Zurich High School

COMPOSITION OF FUNCTIONS

Graph of Secant, Cosecant, and Cotangent

Warm-up: (1 − sin 2 x) sec 2 x = cos 2 x sec 2 x = 1

Presentation transcript:

Warm Up Determine the derivative of each of the following.

Homework Questions…

The functions f and g are differentiable for all real numbers. The table below gives values of the functions and their first derivatives at selected values of x. d) If h(x) = f(g(x)) + 2, find the value of h(3) and h’(3).

Use the quotient rule to find the derivative of sec(x)

Trig Derivative Summary f(x)f’(x) Sin(x) Cos(x) Tan (x) Cot(x) Sec(x) Csc(x)

Examples…

Write the equation of the tangent line to the graph of y = cot at the point where x =