The Product Rule

Say you have a function like this one:


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The product rule simply states that if the function can be split up into a sub-function multiplied by another sub-function, then:


Here u and v are the sub-functions, and  and  are their derivatives with respect to x.



Here’s an example of using the product rule:

Product rule question

Find the derivative of  with respect to x.


                                                      Let u = 3x2 + 2x

                                                       Let v = 2x4 – 5.






This you can then expand out and simplify to give:


Handy Hint #1 -  Writing letters in calculus

Be careful when you write ‘u’ and ‘v’ – it is easy to mix them up!  You could use the letters ‘a’ and ‘b’ just as easily, ‘u’ and ‘v’ are used here because many textbooks use them.