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Lesson 1 Nov 12 09
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Lesson 1 Nov 12 09

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  • 1. y = 2x ­ 1 Derivative of a Linear Function If f(x) = mx + b where m and b are constants,  then the derivative of f is f '(x) = m
  • 2. y = 4 Derivative of a Constant Function If f(x) = c, where c is a constant, then  f '(x) = 0
  • 3. Function Derivative f(x) = x0 f '(x) = 0 f(x) = x f '(x) = 1 f(x) = x2 f '(x) = 2x What if the exponent is negative? eg. f(x) = x­1
  • 4. 1 ­ 1 d 1) lim x ( x + h dx x = h      0 h
  • 5. The Power Rule If n is any real number, then  d (xn) = nxn ­ 1 f '(x) =      dx
  • 6. Using the Power rule find the derivative for each of the  following functions:  y = x2 + x­5 s = t3/4 ­ t­3 dy ds dx dt
  • 7. The Constant Multiple Rule If c is any constant and f is a differentiable function,  then . . d [c  f(x)] = c  f '(x) dx Function Derivative y = 4 x2 f ' (x) =  f(x) = ­2x­2 f ' (x) = 
  • 8. The Sum and Difference Rule d [f(x) + g(x)] =  f '(x) + g '(x) dx d [f(x) ­ g(x)] =  f '(x) ­ g '(x) dx Given the function: f(x) = 3x4 + 2x3 ­ 3x2 + 9 Find f '(x)
  • 9.  f(x) = 3x4 + 2x3 ­ 3x2 + 9 d  (3x4 + 2x3 ­ 3x2 + 9) dx
  • 10. Exercise 4.1 Odd questions  1 ­ 19