1 / 22

Mastering Derivatives: Power Rule and Anti-Chain Rule Explained

This guide focuses on differentiating various functions using the Power Rule and the Anti-Chain Rule. It covers key concepts such as the differentiation of polynomials and trigonometric functions. Learn how to apply the derivatives of complex expressions step-by-step, including working with functions like ( tan(x) ) and ( sin(x) ). This resource is perfect for students seeking to strengthen their understanding of calculus and improve their differentiation skills through practical examples.

palani
Télécharger la présentation

Mastering Derivatives: Power Rule and Anti-Chain Rule Explained

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. = • (7x+2)13/13 • (7x+2)13/13 + C • (7x+2)11/13 + C • (7x+2)11/11 + C

  2. .

  3. . u = 2x-3 du/dx = 2 du = 2 dx du/2 = dx

  4. Power Rule • If u is any differentiable function and n is not -1, then

  5. Let u = the bad stuff • Using the power rule • u = 1 + z2. • du/dz = 2z or du = 2z dz • z dz = du/2

  6. Let u = the bad stuff • u = 1 + z2. • du/dz = 2z • z dz = du/2

  7. u = du/df = 7 or du = 7 df Anti Chain Rule

  8. . u = du/dx = du = 3x2dx x2dx = du/3

  9. sin(3x)dx u = • sin 3x • x • 3x • Cos 3x

  10. (2x-3)3dx u = • 2x-3 • 2x • 3x • 2

  11. (2x-3)3dx = • (2x-3)4/4 + c • (2x-3)4/6 + c • (2x-3)4/8 + c • 2(2x-3)4 + c

  12. x sec2(3x2)dx u = • sec 3x2 • 3x • 3x2 • x

  13. x sec2(3x2)dx • tan 3x2 + c • tan 3x2/ 3 + c • sec 3x2/ 3 + c • tan 3x2/ 6 + c

  14. = • 0.333333 • 0.1

  15. = • 0.2 • 0.1

  16. Copy g(x) If derivative is here Add one to exponent Divide by new exponent Anti Power Rule

  18. = • -10.0 • 0.1

  19. = • 0.5 • 0.1

  20. What is the derivative of tan(x)?

  21. What is the derivative of tan(x)?

  22. Copy sin(x) Derivative is here Add one to exponent Divide by new exponent Anti Power Rule

More Related