Consider the function

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

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

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

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

6. product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

7. Example:

10. Try this:

11. Try this:

16. quotient rule: or

17. Quotient Rule