What is the chain rule??

• If?y?is a function of?u, and?u?is a function of?x, then the?chain rule?tells us that

• The chain rule allows us to differentiate more complicated expressions and?composite functions
• You will often see and use the?chain rule?with different variables
  • This is particularly useful for?connected rates of change

How do I differentiate (ax?+?b)ⁿ?

• For?n = 2?you will most likely?expand the brackets?and differentiate each term separately
• If?n > 2?this becomes?time-consuming?and if?n?is not a positive integer we need a different method completely
• The chain rule allows us to use?substitution?to differentiate any function in the form?y?= (ax?+?b)ⁿ
  • Let?u = ax + b,?then?y = uⁿ
  • Differentiate?both parts?separately
  • • 

How do I differentiate?√(ax+b)?

• This method can be used for any fractional power?of any linear or non-linear expression
• • Provided you know how to differentiate the non-linear expression

How do I differentiate (f(x))ⁿ?

• This method can be used for any linear or non – linear expression
  • Let?u?= f(x) and follow the method above
• With practice you will be able to carry out this method?without the need for?u
  • This is essential for learning the?reverse chain rule?later in the course