Remember.....
y = log 2 x is the inverse of y = 2x
y = log 10 x is the inverse of y = 10x
y = log e x is the inverse of y = ex
= ln x
Apr 15­5:38 PM
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5.2: Derivatives of Exponential Functions using "lnb"
In general:
f(x) = bx
f'(x) = (lnb) x bx
and
f(x) = bg(x)
f'(x) = (lnb) x bg(x) x g'(x)
Remember that,
f(x) = ex
f'(x) = ex
= ex x ln e
Example 1: Determine the derivative.
a) f(x) = 5x
b) f(x) = 53x-2
Apr 15­12:10 PM
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Example 2:
The population of Goldrush town was 50 000 in 1850. The population
can be modelled by P(t) = 50 000 (0.98)t, where t is the years since
1850.
a) What was the population in 1900?
b) At what rate was it changing in 1900?
Homework: pg. 240 #1, 2, 3, 6
Apr 9­11:13 PM
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