Finding the rate of change by the use of the product rule and the chain rule

Target group : Year 13/Core 3
Learning outcome:
à applying both product rule and chain rule for finding the rate of change.
àExercising skills with an exercise that looks slightly different to the ones they are used to but within the set of the possible exam questions.

QUESTION

Comments:

1.  The formulae issue:

You may face difficulty in applying the product rule here, because you may have not realised that a and b behave like u and v in the formula of the product rule which you are aware of. 
May be it would be better if you learn the product rule in a wordy version (the derivative of the product equals the derivative of the first (factor) times the second one plus the first times the derivative of the second)

 2.       Implicit differentiation - chain rule-rate of change:

One method and one term.

The set of exercises that combine them are quite challenging.