1. Bell-ringer 11/2/09 Suppose that functions f and g and their derivatives with respect to x have the following values at x=0 and x=1. 1.Evaluate the derivative of f(g(x)) at x=0 2.Evaluate the derivative of g(f(x)) at x=0 3.Evaluate the derivative of f(x+g(x)) at x=0

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

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

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

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

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