Differentiating Inverse Functions (DP IB Analysis & Approaches (AA)): Revision Note

Differentiating Inverse Functions

What is meant by an inverse function?

• Some functions are easier to process with  (rather than ) as the subject

  • i.e.  in the form

• This is particularly true when dealing with inverse functions

  • e.g.  If  the inverse would be written as

    • finding can be awkward

    • so write  instead

How do I differentiate inverse functions?

• Since it is easier to differentiate “ with respect to ” rather than “ with respect to ”

  • i.e.  find rather than 

  • Note that will be in terms of  but can be substituted

STEP 1
For the function , the inverse will be

Rewrite this as

STEP 2
From find 

STEP 3
Find  using - this will usually be in terms of 

• If an algebraic solution in terms of  is required substitute  for  in

• If a numerical derivative (e.g. a gradient) is required then use the -coordinate

  • If the -coordinate is not given, you should be able to work it out from the orginal function and -coordinate