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# Lesson 4 Nov 17 09

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### 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