Differentiation of the ln of an ln
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We wish to find
.
What mathematical term from algebra describes this application of a function, to the result of another function?
Composition of functions
.
To take the derivative of
f
, what rules of differentiation
do we need beside the Rule for ln:
?
We need to use the
Chain Rule
to take care of the composition of the functions.
What do we differentiate first?
We start on the “outer” function first. To see that more clearly, set up
w
to represent the inner function.
Rewrite our problem in terms of
w
.
Do the indicated differentiation.
We get
Eventually, we need to convert this back to an expression in
x
. We already have our definition, , to use for that purpose. We also need the derivative of
w
. Find it.
Complete the differentiation.
Combine these results to solve the problem in terms of
x
.
We get
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General Contents
Detailed Contents
Index