We use the product rule when we have 2 functions multiplied together. Don’t be on the lookout for a multiplication sign because there often won’t be one. Instead look for any instances of two different functions of x next to each other
The formula for the product rule is provided in the formula sheet:
When you are looking at the product rule, all you are doing is breaking a complicated function down to simpler functions, that we can easily differentiate.
Let’s look at 2014 exam 1 Q1a
We need to separate this function into two functions and set one as u and one as v, it doesn’t effect the final result which we set to u and which we set to v.
It is important to define the terms before we start using them. If you didn’t spell out what u is equal to, the examiner doesn’t know what u is and where it came from.
Using our basic power and trigonometric differentiation rules we can work out that:
All we have to do now is substitute these values into our original formula:
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