1. Warmup 11/29/16 Objective Tonight’s Homework
How well do you relate to other people? What do you think is the key to a successful friendship?
Objective Tonight’s Homework
To summarize differentials up to this point
pp 256: 5, 7, 9, 15

2. Homework Help
Let’s spend the first 10 minutes of class going over any problems with which you need help. 2

3. Notes on Proving Trigonometric Derivatives
We’ve talked about trig derivatives before:
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)

4. Notes on Proving Trigonometric Derivatives
We’ve talked about trig derivatives before:
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)
But how do we prove these?

5. Notes on Proving Trigonometric Derivatives
We’ve talked about trig derivatives before:
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx tan(x) = sec2(x)
But how do we prove these?
Let’s start by proving d/dx cos(x) = -sin(x)
We’re going to do this by assuming that d/dx sin(x) = cos(x)
We also will use the idea that cos(x)=sin(π/2-x)

6. Notes on Proving Trigonometric Derivatives
Knowing all this, try to prove that: d/dx cos(x) = -sin(x)

7. Notes on Proving Trigonometric Derivatives
Knowing all this, try to prove that: d/dx cos(x) = -sin(x)
y = cos (x) start function
y = sin(π/2-x) Other angle substitution
u = π/2-x U definition
du = -1 dx implicit differentiation
y = sin(u) U substitution
dy = cos(u) du implicit differentiation
dy = cos(π/2-x)(-1) dx substitution back
dy = sin(x)(-1) dx Other angle substitution
dy/dx = -sin(x) Rearranging π/2-x

8. Notes on Proving Trigonometric Derivatives
We’ve now seen quite a number of rules. The rest of this section goes over much the same.
There is a table on page 255 of your book. Copy this table down in your notes

9. Group Practice
Look at the example problems on pages 253 through 255. Make sure the examples make sense. Work through them with a friend.
Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help!
pp 256: 5, 7, 9, 15 9

10. Exit Question Does a function like Arcsin(x) have an integral? a) Yes
b) Yes, but not at all values
c) No
d) Not enough information
e) None of the above