Calculus Methods
21 Handling ax and logax
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We
already know how to handle 
and 
when taking
derivatives and integrals,
but 
and 
are different.
1)
To work with 
, rewrite it first in a
form we can deal with: 
.
1A) Taking the derivative:
If you want to remember a shortcut: take the derivative
as you would if the
function were 
, but then multiply
by the natural log of the actual base.
1B) Taking an antiderivative:
If you want to remember a shortcut: take the
antiderivative as you would if the
function were 
, but
then divide by the natural log of the actual base.
2)
To work with 
, rewrite as a natural
log: 
.
Remember that 
is simply a constant, so this is now just as if
you were dealing with 
.
Example
#1: Find the derivative of 
.
1)
1A)
Example
#2: Find the derivative of 
.
2)
