1 / 13

DT.01.5 - Differentiation Techniques: Combining the Differentiation Rules

DT.01.5 - Differentiation Techniques: Combining the Differentiation Rules. MCB4U - Santowski. (A) Review – Differentiation Rules. (1) The Constant Rule  d/dx (k) = 0 (2) The Constant Multiple Rule  d/dx (k × f(x)) = k × f`(x) (3) The Sum and Difference Rules

vidar
Download Presentation

DT.01.5 - Differentiation Techniques: Combining the Differentiation Rules

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. DT.01.5 - Differentiation Techniques: Combining the Differentiation Rules MCB4U - Santowski

  2. (A) Review – Differentiation Rules • (1) The Constant Rule •  d/dx (k) = 0 • (2) The Constant Multiple Rule •  d/dx (k × f(x)) = k × f`(x) • (3) The Sum and Difference Rules •  d/dx [f(x) + g(x)] = f`(x) + g`(x) • (4) The Product Rule •  d/dx [f(x)×g(x)] = f(x)×g`(x) + g(x)×f`(x) • (5) The Quotient Rule •  d/dx [f(x) ÷ g(x)] = f`(x)]×g(x) – g`(x)×f(x) ÷ [g(x)]2 • (6) The Chain Rule • d/dx [f(g(x))] = f`(g(x)) × g`(x)

  3. Find the following: (i) F `(4) if F(x) = f(x) + g(x) (ii) F `(1) if F(x) = fg(x) (iii) F `(-4) if F(x) = f(x) - g(x) (iv) F `(1) if F(x) = f(x) ÷ g(x) (v) F `(-2) if F(x) = g(x) ÷ f(x) (B) Application – Derivative Rules

  4. (f) Find the following: (i) F `(3) if F(x) = 2f(x) - 3g(x) (ii) F `(x) if F(x) = 1 ÷ f(x) (iii) F `(-1) if F(x) = ½ f(x) + ¼g(x) (iv) F `(-2) if F(x) = g(x²) (v) F `(1) if F(x) = g(2x - 3) (vi) F `(-3) if F(x) = f(g(x)) (vii) F `(1) if F(x) = g(f(x)) (B) Application – Derivative Rules

  5. (B) Application – Derivative Rules • (a) Find F `(2) if F(x) = f(x) + g(x) • (b) Find F `(4) if F(x) = fg(x) • (c) Find F `(1) if F(x) = f(x) ÷ g(x) • (d) Find F `(1) if F `(x) = f(x² + 3x)

  6. (B) Application – Derivative Rules • (e) Find F `(5) if F(x) = f(g(x)) • (f) Find F `(3) if F(x) = 2f(x) - 3g(x) • (g) Find F `(1) if F(x) = g(f(x)) • (h) Find F `(2) if F(x) = g(x) ÷ f(x)

  7. (C) Review – Derivatives • (1) Derivatives of Power Functions •  If f(x) = xn then f `(x) = nxn-1 • (2) Derivatives of Primary Trigonometric Functions •  if f(x) = sin(x) then f `(x) = cos(x) •  if f(x) = cos(x) then f `(x) = -sin(x) •  if f(x) = tan(x) then f `(x) = sec2(x) = 1/cos2(x)

  8. (D) Examples • ex 1. Find the derivative of • ex 2. Find the derivative of • ‘ f(x) = (x² + 3)4(4x - 5)3

  9. (D) Examples • Find the derivative of the following:

  10. (D) Examples • Find the derivative of the following:

  11. (D) Examples • Find the derivative of the following:

  12. (E) Internet Examples • Visual Calculus - Chain Rule • Chain Rule from UC Davis

  13. (F) Homework • Handouts from Stewart, 1997, Chap 3.5, Q1-10,18-29

More Related