We use this rule when we wish to divide one function by another. The ‘generic’ expression for the quotient rule looks a little bit more complicated than for the product rule:


If we consider our functions ‘u’ and ‘v’ then the quotient rule states:



Example:


Let u = sin(x) and v=x:





It is important to simply the answer as far as possible and although in the step I have highlighted in blue you would expect the answer to be portrayed with the cosine function first it seems to be a mathematical nuance to display the squared power in the sine function denominator first (although if you left it as I did in blue and then cancelled out the x in the cosine expression you would not, I would think at least, lose any marks for that).


Let’s take a look at another example:



In the table of standard derivatives I gave you earlier, unfortunately I didn’t include the derivative of which is in fact. You will need to know this to attempt the example above. We work through the problem in exactly the same way as before:














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Go To >> Table Of Standard Derivatives And Integrals <<

Have a go at these examples: