Warm Up

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

Homework Answers

The Product and Quotient Rules for Differentiation

Let’s start with the Product Rule…

Leave the first alone

Derivative of the

second

df x g x f x g' x f ' x g x

dxDerivative of the first

Leave the second alone

Examples…Find the derivative, f’(x)

f (x) (2x 1)(3x 4)

Examples…Find the derivative, f’(x)

5f (x) x cosx

Examples…Find the derivative, f’(x)

3f x x x 3

Examples…Find the derivative, f’(x)

f x (x 1)(3x 2)(2x 5)

Examples…Find the derivative, y’

y 2xcosx 2sinx

The Quotient Rule

2

f x g x f ' x f x g' xd, g x 0

dx g x g x

“low d high minus high d low over low low”

Examples…Find the derivative, f’(x)

(2x 1)f(x)

(3x 4)

Examples…Find the derivative, P’(t)

2

4tP(t)

50 t

Examples…Find the derivative, dy/dx

2x 5y

x

Use the quotient rule to derive the formula for the derivative of y = tan(x)

Use the quotient rule to derive the formula for the derivative of y = cot(x)

Use the quotient rule to derive the formula for the derivative of y = csc(x)

Use the quotient rule to derive the formula for the derivative of y = sec(x)

Examples…Find the derivative, f’(x)

4f (x) 3x tanx

Examples…Find the derivative, f’(x)

2

3cscxf(x)

x 1

Write an equation of the line tangent

2x 1to the graph of f (x) = at the

x 3point (2, 3/ 5).

QUIZ MONDAY

Homework worksheet (pg 124 – 125)

#s 5, 6, 8, 15, 25, 35, 39, 43, 45, 50, 53, 62, 63, 66, 67