1. Winter wk 6 – Tues.8.Feb.05 Calculus Ch.3 review:
Polynomial rule for derivatives
Differentiating exponential functions
Chain rule and product rule
3.5 Trigonometric functions
3. 6 Applications of chain rule
Energy Systems, EJZ

2. Differentiating polynomials and ex
Integrating polynomials:
Slope of ex increases exponentially:
d/dx(ex) = ex
d/dx(ax) = ln(a) ax

3. Review chain rule Differentiate exponential function y=eax
Differentiate y=ex2=ez z=x2

4. Review product rule and quotient rule
If y(x) = f(x) g(x) then
Practice: y = x2 e-3x =f.g where f=______, g=______
If y(x) = f(x) / g(x) then

5. Differentiating trig functions
Sketch the slope of y=sin(x)
Does this look familiar?

6. Differentiating cosine
Sketch the slope of y=cos(x)
Does this look familiar?

7. Conceptest 1

8. Conceptest 1 solution

9. Conceptest 2

10. Conceptest 2 solution

11. (Hint: where is df/dx=0?)
Conceptest 3
(Hint: where is df/dx=0?)

12. Conceptest 3 solution

13. (Hint: calculate the slope)
Conceptest 4
(Hint: calculate the slope)

14. Conceptest 4 solution

15. Differentiating tangent
tan(x) = sin(x)/cos(x)
1. Use identity sin2x+cos2x=1 to derive tan2x+1=_____
2. Use product or quotient rule to find d(tan(x))/dx

16. Practice differentiating trig functions
Drill on Ch.3.5 odd # problems through 41 (p.131)
(skip #19)
#5: y = sin(3x) = sin z where z=__________

17. 3.6: Applications of the chain rule
Finding the derivative of an inverse function (133)
What is df/dx if f=x½? Trick: Write f2=x
Differentiate
Solve for df/dx=
(Compare to result from polynomial rule.)

18. Using chain rule to find d/dx(lnx)
Recall that elnx=x. Differentiate
Practice p.136 on odd problems through #15

19. Using chain rule to find d/dx(ax)
Recall that ln(ax)=x ln a. Differentiate
Practice p.136 odd problems thru #35 (skip arc_ probs)

20. Chain rule for related rates
Practice p.137 #46, 48