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

2. quotient rule: or

3. Higher Order Derivatives: is the first derivative of y with respect to x. is the second derivative. (y double prime) is the third derivative.is the fourth derivative. We will learn later what these higher order derivatives are used for. 

4. Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2001 London Bridge, Lake Havasu City, Arizona 3.5 Derivatives of Trig Functions

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

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

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

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