1 / 20

Winter wk 6 – Tues.8.Feb.05

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. Differentiating polynomials and e x.

tilden
Download Presentation

Winter wk 6 – Tues.8.Feb.05

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


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

  12. Conceptest 3 solution

  13. 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

More Related