Differentiate exponential
Functions
f(x) = 2x




slope ­ always positive   f ' is positive
      ­ increasing            increasing
Calculate the derivative of f(x) = bx

       f '(x) =  lim f(x + h) ­ f(x)
                  h      0
                   ...
lim        bx . bh ­ bx
=   h      0
                    h

    lim             bh ­ 1
                    x 
=           ...
lim        bh ­ 1
h      0
             h
f(x) = 2x




f '(x) = ln2 (2x)
f(x) = 3x




f '(x) = ln3 (3x)
Find the derivative of  f(x) = ex


   d (ex)
          = ln e (ex)
   dx
            = ex

                             f...
.
Given   f(x) = 3  4x + 7ex


  find    d    (f(x))
          dx
Exercise 4.2

           odd questions 

1 ­ 21 
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Lesson 3 Nov 16 09

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Lesson 3 Nov 16 09

  1. 1. Differentiate exponential Functions
  2. 2. f(x) = 2x slope ­ always positive f ' is positive ­ increasing increasing
  3. 3. Calculate the derivative of f(x) = bx f '(x) =  lim f(x + h) ­ f(x) h      0 h x + h lim b ­ bx = h      0 h
  4. 4. lim bx . bh ­ bx = h      0 h lim bh ­ 1 x  = b   h      0 h =b x   lim bh ­ 1 h      0 h
  5. 5. lim bh ­ 1 h      0 h
  6. 6. f(x) = 2x f '(x) = ln2 (2x)
  7. 7. f(x) = 3x f '(x) = ln3 (3x)
  8. 8. Find the derivative of  f(x) = ex d (ex) = ln e (ex) dx = ex f '(x) = ex
  9. 9. . Given   f(x) = 3  4x + 7ex find  d (f(x)) dx
  10. 10. Exercise 4.2 odd questions  1 ­ 21 

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