Given     f(x) = x3   g(x) = x5

            .
Find f '(x)   g '(x)                  f '(x) = 3x2   g '(x) = 5x4
The Product Rule

        .                            .
 d [f(x)  g(x)] = f(x)  g '(x) + g(x)  f '(x)
                   ...
2        3
Find the derivative of  f(x) =  (x  + 2) (x  ­ 3)

1) Use the product rule
2        3
Find the derivative of  f(x) =  (x  + 2) (x  ­ 3)

2) Multiply then differentiate
Quotient Rule
                     q(x) = f(x)
                            g(x)

                g(x) . q(x) = f(x)
The Quotient Rule

d [  f(x)  ]       .              .
               g(x)  f '(x) ­ f(x)  g '(x)
             =
dx g(x)  ...
Derivatives of Trigonometric Functions

                   Sine Function




                     d sin(x)  cos(x)
       ...
Cosine Function




d (cos x) = ­ sin(x) 
dx
Derivatives of Trig Functions
d (sin x) = cos(x)      d (csc x) = ­ cscx cotx
dx                      dx

d ( cos x) = ­ s...
Exercise 4.3

          Questions 1 ­ 23

Odd numbers
Lesson 4 Nov 17 09
Upcoming SlideShare
Loading in...5
×

Lesson 4 Nov 17 09

262

Published on

Published in: Education, Sports
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
262
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Lesson 4 Nov 17 09

  1. 1. Given f(x) = x3 g(x) = x5 . Find f '(x)   g '(x) f '(x) = 3x2 g '(x) = 5x4
  2. 2. The Product Rule . . d [f(x)  g(x)] = f(x)  g '(x) + g(x)  f '(x) . dx
  3. 3. 2 3 Find the derivative of  f(x) =  (x  + 2) (x  ­ 3) 1) Use the product rule
  4. 4. 2 3 Find the derivative of  f(x) =  (x  + 2) (x  ­ 3) 2) Multiply then differentiate
  5. 5. Quotient Rule q(x) = f(x) g(x) g(x) . q(x) = f(x)
  6. 6. The Quotient Rule d [  f(x)  ] . . g(x)  f '(x) ­ f(x)  g '(x) = dx g(x)   [g(x)]2
  7. 7. Derivatives of Trigonometric Functions Sine Function d sin(x)  cos(x) = dx
  8. 8. Cosine Function d (cos x) = ­ sin(x)  dx
  9. 9. Derivatives of Trig Functions d (sin x) = cos(x) d (csc x) = ­ cscx cotx dx dx d ( cos x) = ­ sin(x) d (sec x) secx tanx  = dx dx d (tan x) = sec2 (x) d (cot x) = ­ csc2 x dx dx
  10. 10. Exercise 4.3 Questions 1 ­ 23 Odd numbers
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×