Derivatives of the Exponential and Log Functions
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    Exponential and Log Derivatives 
1) If f(x) = ex, then f '(x) = ex
2) If f(x) = eg(x), then f '(x) = g'(x).eg(x)
3) If f(x) = ln x, then f '(x) = 1/x   (x > 0)
4) If f(x) = ln g(x), then f '(x) = g'(x)/g(x)    [g(x) > 0]
Find the derivative of each function

r(x) = x3 s(x) = ex
r'(x) = 3x2 s'(x) = ex
f '(x) = x3ex + 3x2ex = (x3 + 3x2)ex

Current quizaroo #  C1

 Find each derivative by using the appropriate rule!

1)  f(x) = 3x2(5x2 + 6)  Find f'(x)
a) 15x4 + 18x2
b) 60x3 + 36x
c) 60x2
d) 18x
e) 15x3
 
2)  f(x) = (3x + 7)/(5x + 8)  Find f'(x)
 
a) 15
b) 0
c) 3/5
d) -11/(5x + 8)2
e) 3/(5x + 8)2
3)  f(x) = (3x - 1)(4x + 2)/(2x)  Find f'(x)
a) 6
b) 6/x
c) (6x2 + 1)/x2
d) 12x2/(x + 1)
e) derivative does not exist!
 
4)  f(x) = (2x + 5)6  Find f'(x)
a) 12(2x + 5)5
b) 12
c) 64
d) 6(2x)5
e) 0
5)  f(x) = (2x2 - 3)ex
a) 2ex
b) 3ex
c) 4xex - 3ex
d) (2x2 - 3)ex + 4xex
e) ln x
 
 

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