1. Theorem: The less you know, the more money you make
Proof: We know that a) Time is Money (T=M) b) Knowledge is Power (K=P) and from Physics c) Power = Work / Time (P=W/T)
By substitution, K = W/M
Rearrange the equation and M = W/K, or Money = Work/Knowledge
From this equation, it follows that as knowledge goes to 0, money goes to infinity.

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

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

4. Derivative of y=sinx Use the definition of the derivative
To prove the derivative of y=sinx is y’=cosx.

5. Derivative of y=sinx Shortcut: y’=cosx
The proof of the d(cosx) = -sinx is almost identical

6. Derivative of y=tanx
Use the quotient rule to show the derivative is y’=sec2x
The proof of the d(cotx) = -csc2x is almost identical
Shortcut: y’=sec2x

7. Derivative of y=secx
Use the quotient rule to show the derivative is y’=secxtanx
The proof of the d(cscx) = -cscxcotx is almost identical
Shortcut: y’=secxtanx

8. Summary of trig derivativesp

12. Practice Time
Now for a worksheet