Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2001 London Bridge, Lake Havasu City, Arizona 2.3 Product and Quotient Rules and Derivatives of Trig Functions

Key to 2-2 HW Evens 2) -.5, -112) 322) cosx 4)014) 2t+224) 6)16) 26) 8)18) 28) 10)20)30) 32) 34) 0

Calculus Warm-Up Find a and b such that f is differentiable everywhere.

Calculus Warm-Up

product rule:Notice that this is not just the product of two derivatives. OR

product rule: try this one

product rule: try this one

product rule: try this one

quotient rule:

Determine the point(s) at which the graph of the function has a horizontal tangent line:

Practice Find the derivatives of the following functions:

4 3/4

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

Recall these derivatives?

We can do the same thing for slope The resulting curve is a sine curve that has been reflected about the x-axis.

We can find the derivative of tangent x by using the quotient rule.

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

BC Homework: Day 1: Pg.126: 1-53 odd, 63,67,77 Day 2: MMM 39-41

AB Homework: Day 1: Pg.126: 1-53 odd, 63,65 Day 2: MMM 39-41

Warm-up Find k such that the line is tangent to the graph of the function.

Warm-up Find k such that the line is tangent to the graph of the function.

HWQ Find an equation of the tangent line to the graph at (-1,1).